LMFDB - Embedded newform 220.2.l.d.23.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(23,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.23"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$220 = 2^{2} \cdot 5 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	220.l (of order $4$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [28,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.9
Character	$\chi$	$=$	220.23
Dual form			220.2.l.d.67.9

$q$ -expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.513913 - 1.31753i) q^{2} +(0.912547 - 0.912547i) q^{3} +(-1.47179 - 1.35419i) q^{4} +(1.46492 - 1.68939i) q^{5} +(-0.733342 - 1.67128i) q^{6} +(0.0653068 + 0.0653068i) q^{7} +(-2.54057 + 1.24319i) q^{8} +1.33451i q^{9} +(-1.47298 - 2.79827i) q^{10} +1.00000i q^{11} +(-2.57884 + 0.107310i) q^{12} +(0.473161 + 0.473161i) q^{13} +(0.119606 - 0.0524819i) q^{14} +(-0.204839 - 2.87845i) q^{15} +(0.332318 + 3.98617i) q^{16} +(-1.01081 + 1.01081i) q^{17} +(1.75827 + 0.685824i) q^{18} -2.65097 q^{19} +(-4.44380 + 0.502637i) q^{20} +0.119191 q^{21} +(1.31753 + 0.513913i) q^{22} +(5.32132 - 5.32132i) q^{23} +(-1.18392 + 3.45286i) q^{24} +(-0.708046 - 4.94961i) q^{25} +(0.866568 - 0.380242i) q^{26} +(3.95545 + 3.95545i) q^{27} +(-0.00767967 - 0.184556i) q^{28} +5.94796i q^{29} +(-3.89772 - 1.20939i) q^{30} -1.44287i q^{31} +(5.42270 + 1.61070i) q^{32} +(0.912547 + 0.912547i) q^{33} +(0.812306 + 1.85124i) q^{34} +(0.205997 - 0.0146594i) q^{35} +(1.80719 - 1.96412i) q^{36} +(-5.27054 + 5.27054i) q^{37} +(-1.36237 + 3.49274i) q^{38} +0.863563 q^{39} +(-1.62148 + 6.11317i) q^{40} -5.13952 q^{41} +(0.0612538 - 0.157038i) q^{42} +(4.06096 - 4.06096i) q^{43} +(1.35419 - 1.47179i) q^{44} +(2.25451 + 1.95495i) q^{45} +(-4.27633 - 9.74572i) q^{46} +(7.89803 + 7.89803i) q^{47} +(3.94083 + 3.33431i) q^{48} -6.99147i q^{49} +(-6.88515 - 1.61079i) q^{50} +1.84482i q^{51} +(-0.0556408 - 1.33714i) q^{52} +(2.60160 + 2.60160i) q^{53} +(7.24419 - 3.17868i) q^{54} +(1.68939 + 1.46492i) q^{55} +(-0.247105 - 0.0847274i) q^{56} +(-2.41913 + 2.41913i) q^{57} +(7.83664 + 3.05673i) q^{58} -7.70258 q^{59} +(-3.59650 + 4.51386i) q^{60} +7.06915 q^{61} +(-1.90103 - 0.741508i) q^{62} +(-0.0871529 + 0.0871529i) q^{63} +(4.90895 - 6.31682i) q^{64} +(1.49249 - 0.106210i) q^{65} +(1.67128 - 0.733342i) q^{66} +(-5.47540 - 5.47540i) q^{67} +(2.85652 - 0.118865i) q^{68} -9.71192i q^{69} +(0.0865504 - 0.278942i) q^{70} +1.80081i q^{71} +(-1.65906 - 3.39042i) q^{72} +(5.16419 + 5.16419i) q^{73} +(4.23552 + 9.65271i) q^{74} +(-5.16288 - 3.87063i) q^{75} +(3.90166 + 3.58992i) q^{76} +(-0.0653068 + 0.0653068i) q^{77} +(0.443796 - 1.13777i) q^{78} -14.2952 q^{79} +(7.22100 + 5.27799i) q^{80} +3.21553 q^{81} +(-2.64126 + 6.77149i) q^{82} +(-11.9160 + 11.9160i) q^{83} +(-0.175424 - 0.161408i) q^{84} +(0.226896 + 3.18839i) q^{85} +(-3.26347 - 7.43743i) q^{86} +(5.42780 + 5.42780i) q^{87} +(-1.24319 - 2.54057i) q^{88} -5.69673i q^{89} +(3.73433 - 1.96572i) q^{90} +0.0618012i q^{91} +(-15.0380 + 0.625755i) q^{92} +(-1.31668 - 1.31668i) q^{93} +(14.4648 - 6.34702i) q^{94} +(-3.88344 + 4.47850i) q^{95} +(6.41831 - 3.47862i) q^{96} +(-0.398370 + 0.398370i) q^{97} +(-9.21149 - 3.59300i) q^{98} -1.33451 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$28 q + 2 q^{2} + 4 q^{3} - 4 q^{4} + 2 q^{5} - 12 q^{6} + 2 q^{7} + 2 q^{8} - 6 q^{10} + 8 q^{12} + 6 q^{13} + 20 q^{14} - 8 q^{15} + 8 q^{16} - 14 q^{17} - 6 q^{18} - 4 q^{19} + 8 q^{20} - 16 q^{21} - 2 q^{22}+ \cdots + 20 q^{99}+O(q^{100})$ 28 * q + 2 * q^2 + 4 * q^3 - 4 * q^4 + 2 * q^5 - 12 * q^6 + 2 * q^7 + 2 * q^8 - 6 * q^10 + 8 * q^12 + 6 * q^13 + 20 * q^14 - 8 * q^15 + 8 * q^16 - 14 * q^17 - 6 * q^18 - 4 * q^19 + 8 * q^20 - 16 * q^21 - 2 * q^22 + 8 * q^23 - 28 * q^24 - 4 * q^25 + 4 * q^26 - 44 * q^27 + 8 * q^28 - 24 * q^30 - 38 * q^32 + 4 * q^33 + 52 * q^34 + 10 * q^35 - 4 * q^36 + 20 * q^37 - 48 * q^38 - 32 * q^39 + 46 * q^40 + 12 * q^41 + 32 * q^42 - 2 * q^43 - 10 * q^45 + 4 * q^46 + 44 * q^47 + 44 * q^48 - 18 * q^50 - 52 * q^52 - 28 * q^53 + 40 * q^54 + 2 * q^55 + 4 * q^56 - 8 * q^57 - 36 * q^58 + 16 * q^59 - 32 * q^60 - 12 * q^61 + 20 * q^62 + 10 * q^63 - 28 * q^64 - 30 * q^65 - 16 * q^67 + 68 * q^68 - 40 * q^70 - 38 * q^72 + 22 * q^73 + 20 * q^74 + 56 * q^75 + 4 * q^76 - 2 * q^77 - 40 * q^78 + 20 * q^79 + 12 * q^80 + 12 * q^81 + 12 * q^82 - 2 * q^83 - 120 * q^84 - 14 * q^85 - 20 * q^86 + 48 * q^87 + 14 * q^88 - 10 * q^90 + 4 * q^92 - 20 * q^93 + 20 * q^94 - 92 * q^95 + 40 * q^96 + 16 * q^97 - 82 * q^98 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$ .

$n$	$101$	$111$	$177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	0.513913	−	1.31753i	0.363391	−	0.931637i
$2$	0.513913	−	1.31753i	0.363391	−	0.931637i
$3$	0.912547	−	0.912547i	0.526859	−	0.526859i	−0.392775	−	0.919635i	$-0.628485\pi$
$3$	0.912547	−	0.912547i	0.526859	−	0.526859i	0.919635	+	0.392775i	$0.128485\pi$
$4$	−1.47179	−	1.35419i	−0.735894	−	0.677097i
$5$	1.46492	−	1.68939i	0.655130	−	0.755516i
$5$	1.46492	−	1.68939i	0.655130	−	0.755516i
$6$	−0.733342	−	1.67128i	−0.299386	−	0.682298i
$7$	0.0653068	+	0.0653068i	0.0246837	+	0.0246837i	0.719341	−	0.694657i	$-0.244444\pi$
$7$	0.0653068	+	0.0653068i	0.0246837	+	0.0246837i	−0.694657	+	0.719341i	$0.744444\pi$
$8$	−2.54057	+	1.24319i	−0.898226	+	0.439535i
$9$			1.33451i			0.444838i
$10$	−1.47298	−	2.79827i	−0.465798	−	0.884891i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	−2.57884	+	0.107310i	−0.744448	+	0.0309777i
$13$	0.473161	+	0.473161i	0.131231	+	0.131231i	0.769671	−	0.638440i	$-0.220420\pi$
$13$	0.473161	+	0.473161i	0.131231	+	0.131231i	−0.638440	+	0.769671i	$0.720420\pi$
$14$	0.119606	−	0.0524819i	0.0319660	−	0.0140264i
$15$	−0.204839	−	2.87845i	−0.0528893	−	0.743212i
$16$	0.332318	+	3.98617i	0.0830795	+	0.996543i
$17$	−1.01081	+	1.01081i	−0.245157	+	0.245157i	−0.818980	−	0.573823i	$-0.805460\pi$
$17$	−1.01081	+	1.01081i	−0.245157	+	0.245157i	0.573823	+	0.818980i	$0.305460\pi$
$18$	1.75827	+	0.685824i	0.414428	+	0.161650i
$19$	−2.65097			−0.608173			−0.304087	−	0.952644i	$-0.598351\pi$
$19$	−2.65097			−0.608173			−0.304087	+	0.952644i	$0.598351\pi$
$20$	−4.44380	+	0.502637i	−0.993664	+	0.112393i
$21$	0.119191			0.0260096
$22$	1.31753	+	0.513913i	0.280899	+	0.109567i
$23$	5.32132	−	5.32132i	1.10957	−	1.10957i	0.116367	−	0.993206i	$-0.462875\pi$
$23$	5.32132	−	5.32132i	1.10957	−	1.10957i	0.993206	−	0.116367i	$-0.0371248\pi$
$24$	−1.18392	+	3.45286i	−0.241666	+	0.704812i
$25$	−0.708046	−	4.94961i	−0.141609	−	0.989923i
$26$	0.866568	−	0.380242i	0.169948	−	0.0745715i
$27$	3.95545	+	3.95545i	0.761227	+	0.761227i
$28$	−0.00767967	−	0.184556i	−0.00145132	−	0.0348778i
$29$			5.94796i			1.10451i	0.833676	+	0.552254i	$0.186232\pi$
$29$			5.94796i			1.10451i	−0.833676	+	0.552254i	$0.813768\pi$
$30$	−3.89772	−	1.20939i	−0.711623	−	0.220803i
$31$		−	1.44287i		−	0.259147i	−0.991570	−	0.129573i	$-0.958639\pi$
$31$		−	1.44287i		−	0.259147i	0.991570	−	0.129573i	$-0.0413608\pi$
$32$	5.42270	+	1.61070i	0.958606	+	0.284735i
$33$	0.912547	+	0.912547i	0.158854	+	0.158854i
$34$	0.812306	+	1.85124i	0.139309	+	0.317485i
$35$	0.205997	−	0.0146594i	0.0348199	−	0.00247789i
$36$	1.80719	−	1.96412i	0.301199	−	0.327354i
$37$	−5.27054	+	5.27054i	−0.866472	+	0.866472i	−0.992080	−	0.125608i	$-0.959912\pi$
$37$	−5.27054	+	5.27054i	−0.866472	+	0.866472i	0.125608	+	0.992080i	$0.459912\pi$
$38$	−1.36237	+	3.49274i	−0.221005	+	0.566597i
$39$	0.863563			0.138281
$40$	−1.62148	+	6.11317i	−0.256379	+	0.966576i
$41$	−5.13952			−0.802658			−0.401329	−	0.915934i	$-0.631452\pi$
$41$	−5.13952			−0.802658			−0.401329	+	0.915934i	$0.631452\pi$
$42$	0.0612538	−	0.157038i	0.00945167	−	0.0242315i
$43$	4.06096	−	4.06096i	0.619291	−	0.619291i	−0.326058	−	0.945350i	$-0.605721\pi$
$43$	4.06096	−	4.06096i	0.619291	−	0.619291i	0.945350	+	0.326058i	$0.105721\pi$
$44$	1.35419	−	1.47179i	0.204152	−	0.221880i
$45$	2.25451	+	1.95495i	0.336082	+	0.291427i
$46$	−4.27633	−	9.74572i	−0.630510	−	1.43693i
$47$	7.89803	+	7.89803i	1.15205	+	1.15205i	0.986142	+	0.165903i	$0.0530540\pi$
$47$	7.89803	+	7.89803i	1.15205	+	1.15205i	0.165903	+	0.986142i	$0.446946\pi$
$48$	3.94083	+	3.33431i	0.568809	+	0.481267i
$49$		−	6.99147i		−	0.998781i
$50$	−6.88515	−	1.61079i	−0.973708	−	0.227801i
$51$			1.84482i			0.258326i
$52$	−0.0556408	−	1.33714i	−0.00771598	−	0.185428i
$53$	2.60160	+	2.60160i	0.357357	+	0.357357i	0.862838	−	0.505481i	$-0.168685\pi$
$53$	2.60160	+	2.60160i	0.357357	+	0.357357i	−0.505481	+	0.862838i	$0.668685\pi$
$54$	7.24419	−	3.17868i	0.985810	−	0.432564i
$55$	1.68939	+	1.46492i	0.227797	+	0.197529i
$56$	−0.247105	−	0.0847274i	−0.0330208	−	0.0113222i
$57$	−2.41913	+	2.41913i	−0.320422	+	0.320422i
$58$	7.83664	+	3.05673i	1.02900	+	0.401369i
$59$	−7.70258			−1.00279			−0.501395	−	0.865218i	$-0.667180\pi$
$59$	−7.70258			−1.00279			−0.501395	+	0.865218i	$0.667180\pi$
$60$	−3.59650	+	4.51386i	−0.464306	+	0.582737i
$61$	7.06915			0.905112			0.452556	−	0.891736i	$-0.350512\pi$
$61$	7.06915			0.905112			0.452556	+	0.891736i	$0.350512\pi$
$62$	−1.90103	−	0.741508i	−0.241430	−	0.0941716i
$63$	−0.0871529	+	0.0871529i	−0.0109802	+	0.0109802i
$64$	4.90895	−	6.31682i	0.613619	−	0.789603i
$65$	1.49249	−	0.106210i	0.185121	−	0.0131738i
$66$	1.67128	−	0.733342i	0.205720	−	0.0902681i
$67$	−5.47540	−	5.47540i	−0.668927	−	0.668927i	0.288541	−	0.957468i	$-0.406830\pi$
$67$	−5.47540	−	5.47540i	−0.668927	−	0.668927i	−0.957468	+	0.288541i	$0.906830\pi$
$68$	2.85652	−	0.118865i	0.346404	−	0.0144145i
$69$		−	9.71192i		−	1.16918i
$70$	0.0865504	−	0.278942i	0.0103447	−	0.0333399i
$71$			1.80081i			0.213717i	0.994274	+	0.106859i	$0.0340793\pi$
$71$			1.80081i			0.213717i	−0.994274	+	0.106859i	$0.965921\pi$
$72$	−1.65906	−	3.39042i	−0.195522	−	0.399565i
$73$	5.16419	+	5.16419i	0.604422	+	0.604422i	0.941483	−	0.337061i	$-0.109433\pi$
$73$	5.16419	+	5.16419i	0.604422	+	0.604422i	−0.337061	+	0.941483i	$0.609433\pi$
$74$	4.23552	+	9.65271i	0.492369	+	1.12211i
$75$	−5.16288	−	3.87063i	−0.596158	−	0.446942i
$76$	3.90166	+	3.58992i	0.447551	+	0.411792i
$77$	−0.0653068	+	0.0653068i	−0.00744240	+	0.00744240i
$78$	0.443796	−	1.13777i	0.0502500	−	0.128827i
$79$	−14.2952			−1.60833			−0.804167	−	0.594404i	$-0.797388\pi$
$79$	−14.2952			−1.60833			−0.804167	+	0.594404i	$0.797388\pi$
$80$	7.22100	+	5.27799i	0.807332	+	0.590097i
$81$	3.21553			0.357281
$82$	−2.64126	+	6.77149i	−0.291679	+	0.747786i
$83$	−11.9160	+	11.9160i	−1.30795	+	1.30795i	−0.385065	+	0.922889i	$0.625821\pi$
$83$	−11.9160	+	11.9160i	−1.30795	+	1.30795i	−0.922889	+	0.385065i	$0.874179\pi$
$84$	−0.175424	−	0.161408i	−0.0191403	−	0.0176110i
$85$	0.226896	+	3.18839i	0.0246103	+	0.345830i
$86$	−3.26347	−	7.43743i	−0.351909	−	0.801999i
$87$	5.42780	+	5.42780i	0.581921	+	0.581921i
$88$	−1.24319	−	2.54057i	−0.132525	−	0.270825i
$89$		−	5.69673i		−	0.603852i	−0.953331	−	0.301926i	$-0.902370\pi$
$89$		−	5.69673i		−	0.603852i	0.953331	−	0.301926i	$-0.0976296\pi$
$90$	3.73433	−	1.96572i	0.393633	−	0.207205i
$91$			0.0618012i			0.00647853i
$92$	−15.0380	+	0.625755i	−1.56782	+	0.0652394i
$93$	−1.31668	−	1.31668i	−0.136534	−	0.136534i
$94$	14.4648	−	6.34702i	1.49193	−	0.654645i
$95$	−3.88344	+	4.47850i	−0.398433	+	0.459485i
$96$	6.41831	−	3.47862i	0.655066	−	0.355035i
$97$	−0.398370	+	0.398370i	−0.0404484	+	0.0404484i	−0.727042	−	0.686593i	$-0.759105\pi$
$97$	−0.398370	+	0.398370i	−0.0404484	+	0.0404484i	0.686593	+	0.727042i	$0.259105\pi$
$98$	−9.21149	−	3.59300i	−0.930501	−	0.362948i
$99$	−1.33451			−0.134124
$100$	−5.66064	+	8.24361i	−0.566064	+	0.824361i
$101$	−11.2570			−1.12012			−0.560058	−	0.828453i	$-0.689221\pi$
$101$	−11.2570			−1.12012			−0.560058	+	0.828453i	$0.689221\pi$
$102$	2.43061	+	0.948076i	0.240666	+	0.0938735i
$103$	4.87406	−	4.87406i	0.480255	−	0.480255i	−0.424958	−	0.905213i	$-0.639711\pi$
$103$	4.87406	−	4.87406i	0.480255	−	0.480255i	0.905213	+	0.424958i	$0.139711\pi$
$104$	−1.79033	−	0.613866i	−0.175556	−	0.0601946i
$105$	0.174605	−	0.201360i	0.0170397	−	0.0196507i
$106$	4.76469	−	2.09070i	0.462787	−	0.203067i
$107$	−2.18565	−	2.18565i	−0.211295	−	0.211295i	0.593523	−	0.804817i	$-0.297737\pi$
$107$	−2.18565	−	2.18565i	−0.211295	−	0.211295i	−0.804817	+	0.593523i	$0.797737\pi$
$108$	−0.465136	−	11.1780i	−0.0447578	−	1.07561i
$109$		−	9.51113i		−	0.911001i	−0.890235	−	0.455501i	$-0.849460\pi$
$109$		−	9.51113i		−	0.911001i	0.890235	−	0.455501i	$-0.150540\pi$
$110$	2.79827	−	1.47298i	0.266805	−	0.140443i
$111$			9.61924i			0.913018i
$112$	−0.238622	+	0.282027i	−0.0225476	+	0.0266490i
$113$	−11.0768	−	11.0768i	−1.04201	−	1.04201i	−0.999078	−	0.0429352i	$-0.986329\pi$
$113$	−11.0768	−	11.0768i	−1.04201	−	1.04201i	−0.0429352	−	0.999078i	$-0.513671\pi$
$114$	1.94406	+	4.43051i	0.182078	+	0.414955i
$115$	−1.19448	−	16.7851i	−0.111386	−	1.56521i
$116$	8.05469	−	8.75414i	0.747859	−	0.812801i
$117$	−0.631440	+	0.631440i	−0.0583767	+	0.0583767i
$118$	−3.95845	+	10.1484i	−0.364405	+	0.934237i
$119$	−0.132025			−0.0121027
$120$	4.09887	+	7.05823i	0.374174	+	0.644326i
$121$	−1.00000			−0.0909091
$122$	3.63293	−	9.31384i	0.328910	−	0.843236i
$123$	−4.69005	+	4.69005i	−0.422888	+	0.422888i
$124$	−1.95392	+	2.12359i	−0.175467	+	0.190704i
$125$	−9.39903	−	6.05460i	−0.840675	−	0.541540i
$126$	0.0700379	+	0.159616i	0.00623947	+	0.0142197i
$127$	2.77907	+	2.77907i	0.246603	+	0.246603i	0.819575	−	0.572972i	$-0.194210\pi$
$127$	2.77907	+	2.77907i	0.246603	+	0.246603i	−0.572972	+	0.819575i	$0.694210\pi$
$128$	−5.79985	−	9.71400i	−0.512639	−	0.858604i
$129$		−	7.41164i		−	0.652559i
$130$	0.627074	−	2.02099i	0.0549981	−	0.177253i
$131$			5.82054i			0.508543i	0.967133	+	0.254272i	$0.0818357\pi$
$131$			5.82054i			0.508543i	−0.967133	+	0.254272i	$0.918164\pi$
$132$	−0.107310	−	2.57884i	−0.00934013	−	0.224459i
$133$	−0.173126	−	0.173126i	−0.0150119	−	0.0150119i
$134$	−10.0279	+	4.40015i	−0.866279	+	0.380115i
$135$	12.4767	−	0.887880i	1.07382	−	0.0764165i
$136$	1.31140	−	3.82465i	0.112451	−	0.327961i
$137$	−4.96234	+	4.96234i	−0.423961	+	0.423961i	−0.886565	−	0.462604i	$-0.846915\pi$
$137$	−4.96234	+	4.96234i	−0.423961	+	0.423961i	0.462604	+	0.886565i	$0.346915\pi$
$138$	−12.7958	−	4.99108i	−1.08925	−	0.424869i
$139$	−19.6363			−1.66553			−0.832765	−	0.553626i	$-0.813244\pi$
$139$	−19.6363			−1.66553			−0.832765	+	0.553626i	$0.813244\pi$
$140$	−0.323036	−	0.257385i	−0.0273015	−	0.0217530i
$141$	14.4146			1.21393
$142$	2.37263	+	0.925462i	0.199107	+	0.0776630i
$143$	−0.473161	+	0.473161i	−0.0395677	+	0.0395677i
$144$	−5.31960	+	0.443483i	−0.443300	+	0.0369569i
$145$	10.0484	+	8.71326i	0.834474	+	0.723597i
$146$	9.45793	−	4.15005i	0.782743	−	0.343460i
$147$	−6.38005	−	6.38005i	−0.526217	−	0.526217i
$148$	14.8945	−	0.619783i	1.22432	−	0.0509458i
$149$			23.2803i			1.90719i	0.301087	+	0.953597i	$0.402651\pi$
$149$			23.2803i			1.90719i	−0.301087	+	0.953597i	$0.597349\pi$
$150$	−7.75296	+	4.81310i	−0.633026	+	0.392988i
$151$		−	7.70843i		−	0.627303i	−0.949538	−	0.313651i	$-0.898448\pi$
$151$		−	7.70843i		−	0.627303i	0.949538	−	0.313651i	$-0.101552\pi$
$152$	6.73495	−	3.29566i	0.546277	−	0.267313i
$153$	−1.34894	−	1.34894i	−0.109055	−	0.109055i
$154$	0.0524819	+	0.119606i	0.00422911	+	0.00963812i
$155$	−2.43756	−	2.11368i	−0.195789	−	0.169775i
$156$	−1.27098	−	1.16943i	−0.101760	−	0.0936295i
$157$	12.9770	−	12.9770i	1.03567	−	1.03567i	0.0363338	−	0.999340i	$-0.488432\pi$
$157$	12.9770	−	12.9770i	1.03567	−	1.03567i	0.999340	−	0.0363338i	$-0.0115679\pi$
$158$	−7.34647	+	18.8344i	−0.584454	+	1.49838i
$159$	4.74816			0.376554
$160$	10.6649	−	6.80148i	0.843134	−	0.537704i
$161$	0.695038			0.0547766
$162$	1.65250	−	4.23656i	0.129833	−	0.332856i
$163$	6.37115	−	6.37115i	0.499027	−	0.499027i	−0.412108	−	0.911135i	$-0.635207\pi$
$163$	6.37115	−	6.37115i	0.499027	−	0.499027i	0.911135	+	0.412108i	$0.135207\pi$
$164$	7.56428	+	6.95991i	0.590671	+	0.543477i
$165$	2.87845	−	0.204839i	0.224087	−	0.0159467i
$166$	9.57597	+	21.8236i	0.743239	+	1.69384i
$167$	12.0038	+	12.0038i	0.928881	+	0.928881i	0.997634	−	0.0687523i	$-0.0219018\pi$
$167$	12.0038	+	12.0038i	0.928881	+	0.928881i	−0.0687523	+	0.997634i	$0.521902\pi$
$168$	−0.302813	+	0.148177i	−0.0233625	+	0.0114321i
$169$		−	12.5522i		−	0.965557i
$170$	4.31742	+	1.33961i	0.331131	+	0.102744i
$171$		−	3.53775i		−	0.270539i
$172$	−11.4762	+	0.477544i	−0.875053	+	0.0364124i
$173$	−5.56357	−	5.56357i	−0.422990	−	0.422990i	0.463242	−	0.886232i	$-0.346686\pi$
$173$	−5.56357	−	5.56357i	−0.422990	−	0.422990i	−0.886232	+	0.463242i	$0.846686\pi$
$174$	9.94071	−	4.36189i	0.753604	−	0.330674i
$175$	0.277003	−	0.369484i	0.0209395	−	0.0279303i
$176$	−3.98617	+	0.332318i	−0.300469	+	0.0250494i
$177$	−7.02897	+	7.02897i	−0.528330	+	0.528330i
$178$	−7.50563	−	2.92762i	−0.562571	−	0.219435i
$179$	4.15446			0.310519			0.155259	−	0.987874i	$-0.450379\pi$
$179$	4.15446			0.310519			0.155259	+	0.987874i	$0.450379\pi$
$180$	−0.670777	−	5.93032i	−0.0499967	−	0.442020i
$181$	−9.46693			−0.703671			−0.351836	−	0.936062i	$-0.614442\pi$
$181$	−9.46693			−0.703671			−0.351836	+	0.936062i	$0.614442\pi$
$182$	0.0814252	+	0.0317604i	0.00603564	+	0.00235424i
$183$	6.45093	−	6.45093i	0.476867	−	0.476867i
$184$	−6.90375	+	20.1346i	−0.508951	+	1.48434i
$185$	1.18308	+	16.6249i	0.0869817	+	1.22229i
$186$	−2.41144	+	1.05811i	−0.176815	+	0.0775848i
$187$	−1.01081	−	1.01081i	−0.0739176	−	0.0739176i
$188$	−0.928759	−	22.3197i	−0.0677367	−	1.62783i
$189$			0.516636i			0.0375797i
$190$	3.90483	+	7.41812i	0.283286	+	0.538167i
$191$			18.6435i			1.34899i	0.738277	+	0.674497i	$0.235640\pi$
$191$			18.6435i			1.34899i	−0.738277	+	0.674497i	$0.764360\pi$
$192$	−1.28475	−	10.2440i	−0.0927189	−	0.739300i
$193$	19.4785	+	19.4785i	1.40209	+	1.40209i	0.793427	+	0.608666i	$0.208295\pi$
$193$	19.4785	+	19.4785i	1.40209	+	1.40209i	0.608666	+	0.793427i	$0.291705\pi$
$194$	0.320139	+	0.729594i	0.0229846	+	0.0523818i
$195$	1.26505	−	1.45889i	0.0905919	−	0.104473i
$196$	−9.46781	+	10.2900i	−0.676272	+	0.734997i
$197$	13.7373	−	13.7373i	0.978743	−	0.978743i	−0.0210356	−	0.999779i	$-0.506696\pi$
$197$	13.7373	−	13.7373i	0.978743	−	0.978743i	0.999779	+	0.0210356i	$0.00669635\pi$
$198$	−0.685824	+	1.75827i	−0.0487394	+	0.124955i
$199$	9.36208			0.663661			0.331830	−	0.943339i	$-0.392334\pi$
$199$	9.36208			0.663661			0.331830	+	0.943339i	$0.392334\pi$
$200$	7.95216	+	11.6946i	0.562302	+	0.826932i
$201$	−9.99313			−0.704861
$202$	−5.78513	+	14.8315i	−0.407041	+	1.04354i
$203$	−0.388442	+	0.388442i	−0.0272633	+	0.0272633i
$204$	2.49824	−	2.71518i	0.174912	−	0.190101i
$205$	−7.52896	+	8.68263i	−0.525845	+	0.606421i
$206$	−3.91689	−	8.92658i	−0.272903	−	0.621944i
$207$	7.10139	+	7.10139i	0.493580	+	0.493580i
$208$	−1.72886	+	2.04334i	−0.119875	+	0.141680i
$209$		−	2.65097i		−	0.183371i
$210$	−0.175566	−	0.333529i	−0.0121152	−	0.0230157i
$211$		−	19.0983i		−	1.31478i	−0.753550	−	0.657390i	$-0.771660\pi$
$211$		−	19.0983i		−	1.31478i	0.753550	−	0.657390i	$-0.228340\pi$
$212$	−0.305932	−	7.35207i	−0.0210115	−	0.504942i
$213$	1.64333	+	1.64333i	0.112599	+	0.112599i
$214$	−4.00290	+	1.75643i	−0.273632	+	0.120067i
$215$	−0.911564	−	12.8095i	−0.0621682	−	0.873601i
$216$	−14.9665	−	5.13170i	−1.01834	−	0.349168i
$217$	0.0942291	−	0.0942291i	0.00639669	−	0.00639669i
$218$	−12.5312	−	4.88789i	−0.848722	−	0.331050i
$219$	9.42513			0.636891
$220$	−0.502637	−	4.44380i	−0.0338878	−	0.299601i
$221$	−0.956549			−0.0643445
$222$	12.6737	+	4.94345i	0.850601	+	0.331783i
$223$	1.52935	−	1.52935i	0.102413	−	0.102413i	−0.654044	−	0.756457i	$-0.726929\pi$
$223$	1.52935	−	1.52935i	0.102413	−	0.102413i	0.756457	+	0.654044i	$0.226929\pi$
$224$	0.248949	+	0.459329i	0.0166336	+	0.0306902i
$225$	6.60533	−	0.944898i	0.440355	−	0.0629932i
$226$	−20.2865	+	8.90151i	−1.34944	+	0.592119i
$227$	−7.50620	−	7.50620i	−0.498204	−	0.498204i	0.412675	−	0.910879i	$-0.364595\pi$
$227$	−7.50620	−	7.50620i	−0.498204	−	0.498204i	−0.910879	+	0.412675i	$0.864595\pi$
$228$	6.83642	−	0.284475i	0.452753	−	0.0188398i
$229$			13.3544i			0.882485i	0.897388	+	0.441243i	$0.145462\pi$
$229$			13.3544i			0.882485i	−0.897388	+	0.441243i	$0.854538\pi$
$230$	−22.7287	−	7.05229i	−1.49869	−	0.465014i
$231$			0.119191i			0.00784220i
$232$	−7.39446	−	15.1112i	−0.485470	−	0.992098i
$233$	4.32195	+	4.32195i	0.283140	+	0.283140i	0.834360	−	0.551220i	$-0.185837\pi$
$233$	4.32195	+	4.32195i	0.283140	+	0.283140i	−0.551220	+	0.834360i	$0.685837\pi$
$234$	0.507438	+	1.15645i	0.0331723	+	0.0755994i
$235$	24.9127	−	1.77287i	1.62513	−	0.115649i
$236$	11.3366	+	10.4308i	0.737948	+	0.678987i
$237$	−13.0450	+	13.0450i	−0.847366	+	0.847366i
$238$	−0.0678494	+	0.173948i	−0.00439803	+	0.0112754i
$239$	25.2845			1.63552			0.817760	−	0.575559i	$-0.195216\pi$
$239$	25.2845			1.63552			0.817760	+	0.575559i	$0.195216\pi$
$240$	11.4059	−	1.77309i	0.736249	−	0.114452i
$241$	−11.0013			−0.708655			−0.354328	−	0.935121i	$-0.615290\pi$
$241$	−11.0013			−0.708655			−0.354328	+	0.935121i	$0.615290\pi$
$242$	−0.513913	+	1.31753i	−0.0330356	+	0.0846942i
$243$	−8.93203	+	8.93203i	−0.572990	+	0.572990i
$244$	−10.4043	−	9.57300i	−0.666066	−	0.612849i
$245$	−11.8113	−	10.2419i	−0.754595	−	0.654332i
$246$	3.76902	+	8.58958i	0.240304	+	0.547652i
$247$	−1.25433	−	1.25433i	−0.0798113	−	0.0798113i
$248$	1.79376	+	3.66570i	0.113904	+	0.232772i
$249$			21.7479i			1.37822i
$250$	−12.8074	+	9.27200i	−0.810012	+	0.586413i
$251$			29.5654i			1.86615i	0.359683	+	0.933075i	$0.382885\pi$
$251$			29.5654i			1.86615i	−0.359683	+	0.933075i	$0.617115\pi$
$252$	0.246293	−	0.0102486i	0.0155150	−	0.000645604i
$253$	5.32132	+	5.32132i	0.334549	+	0.334549i
$254$	5.08973	−	2.23332i	0.319358	−	0.140131i
$255$	3.11661	+	2.70250i	0.195170	+	0.169237i
$256$	−15.7791	+	2.64935i	−0.986196	+	0.165584i
$257$	12.1596	−	12.1596i	0.758496	−	0.758496i	−0.217553	−	0.976049i	$-0.569807\pi$
$257$	12.1596	−	12.1596i	0.758496	−	0.758496i	0.976049	+	0.217553i	$0.0698073\pi$
$258$	−9.76509	−	3.80894i	−0.607948	−	0.237134i
$259$	−0.688405			−0.0427754
$260$	−2.34046	−	1.86480i	−0.145149	−	0.115650i
$261$	−7.93764			−0.491328
$262$	7.66876	+	2.99125i	0.473777	+	0.184800i
$263$	13.5230	−	13.5230i	0.833864	−	0.833864i	−0.154179	−	0.988043i	$-0.549273\pi$
$263$	13.5230	−	13.5230i	0.833864	−	0.833864i	0.988043	+	0.154179i	$0.0492732\pi$
$264$	−3.45286	−	1.18392i	−0.212509	−	0.0728649i
$265$	8.20623	−	0.583981i	0.504104	−	0.0358737i
$266$	−0.317071	+	0.139128i	−0.0194409	+	0.00853047i
$267$	−5.19854	−	5.19854i	−0.318145	−	0.318145i
$268$	0.643873	+	15.4734i	0.0393308	+	0.945188i
$269$		−	1.45696i		−	0.0888322i	−0.999013	−	0.0444161i	$-0.985857\pi$
$269$		−	1.45696i		−	0.0888322i	0.999013	−	0.0444161i	$-0.0141427\pi$
$270$	5.24211	−	16.8947i	0.319025	−	1.02818i
$271$		−	8.56442i		−	0.520251i	−0.965575	−	0.260126i	$-0.916236\pi$
$271$		−	8.56442i		−	0.520251i	0.965575	−	0.260126i	$-0.0837640\pi$
$272$	−4.36516	−	3.69334i	−0.264677	−	0.223942i
$273$	0.0563966	+	0.0563966i	0.00341328	+	0.00341328i
$274$	3.98784	+	9.08825i	0.240914	+	0.549041i
$275$	4.94961	−	0.708046i	0.298473	−	0.0426968i
$276$	−13.1518	+	14.2939i	−0.791647	+	0.860391i
$277$	8.63149	−	8.63149i	0.518616	−	0.518616i	−0.398537	−	0.917152i	$-0.630482\pi$
$277$	8.63149	−	8.63149i	0.518616	−	0.518616i	0.917152	+	0.398537i	$0.130482\pi$
$278$	−10.0913	+	25.8715i	−0.605239	+	1.55167i
$279$	1.92553			0.115278
$280$	−0.505125	+	0.293337i	−0.0301870	+	0.0175303i
$281$	8.37468			0.499592			0.249796	−	0.968299i	$-0.419637\pi$
$281$	8.37468			0.499592			0.249796	+	0.968299i	$0.419637\pi$
$282$	7.40787	−	18.9918i	0.441132	−	1.13094i
$283$	−7.90636	+	7.90636i	−0.469985	+	0.469985i	−0.901910	−	0.431925i	$-0.857835\pi$
$283$	−7.90636	+	7.90636i	−0.469985	+	0.469985i	0.431925	+	0.901910i	$0.357835\pi$
$284$	2.43865	−	2.65042i	0.144707	−	0.157273i
$285$	0.543023	+	7.63067i	0.0321659	+	0.452002i
$286$	0.380242	+	0.866568i	0.0224842	+	0.0512413i
$287$	−0.335646	−	0.335646i	−0.0198125	−	0.0198125i
$288$	−2.14951	+	7.23667i	−0.126661	+	0.426425i
$289$			14.9565i			0.879796i
$290$	16.6440	−	8.76125i	0.977370	−	0.514478i
$291$			0.727064i			0.0426212i
$292$	−0.607276	−	14.5939i	−0.0355381	−	0.854043i
$293$	−7.94335	−	7.94335i	−0.464056	−	0.464056i	0.435927	−	0.899982i	$-0.356421\pi$
$293$	−7.94335	−	7.94335i	−0.464056	−	0.464056i	−0.899982	+	0.435927i	$0.856421\pi$
$294$	−11.6847	+	5.12714i	−0.681466	+	0.299021i
$295$	−11.2836	+	13.0126i	−0.656958	+	0.757625i
$296$	6.83786	−	19.9425i	0.397443	−	1.15913i
$297$	−3.95545	+	3.95545i	−0.229518	+	0.229518i
$298$	30.6725	+	11.9640i	1.77681	+	0.693057i
$299$	5.03568			0.291221
$300$	2.35708	+	12.6883i	0.136086	+	0.732559i
$301$	0.530417			0.0305727
$302$	−10.1561	−	3.96146i	−0.584418	−	0.227956i
$303$	−10.2726	+	10.2726i	−0.590144	+	0.590144i
$304$	−0.880963	−	10.5672i	−0.0505267	−	0.606071i
$305$	10.3557	−	11.9425i	0.592966	−	0.683827i
$306$	−2.47051	+	1.08403i	−0.141229	+	0.0619701i
$307$	−13.3805	−	13.3805i	−0.763666	−	0.763666i	0.213317	−	0.976983i	$-0.431573\pi$
$307$	−13.3805	−	13.3805i	−0.763666	−	0.763666i	−0.976983	+	0.213317i	$0.931573\pi$
$308$	0.184556	−	0.00767967i	0.0105160	−	0.000437590i
$309$		−	8.89562i		−	0.506054i
$310$	−4.03753	+	2.12532i	−0.229317	+	0.120710i
$311$		−	32.5214i		−	1.84412i	−0.387046	−	0.922060i	$-0.626505\pi$
$311$		−	32.5214i		−	1.84412i	0.387046	−	0.922060i	$-0.373495\pi$
$312$	−2.19394	+	1.07357i	−0.124207	+	0.0607792i
$313$	−14.8992	−	14.8992i	−0.842150	−	0.842150i	0.146988	−	0.989138i	$-0.453042\pi$
$313$	−14.8992	−	14.8992i	−0.842150	−	0.842150i	−0.989138	+	0.146988i	$0.953042\pi$
$314$	−10.4285	−	23.7666i	−0.588517	−	1.34123i
$315$	0.0195632	+	0.274906i	0.00110226	+	0.0154892i
$316$	21.0395	+	19.3584i	1.18356	+	1.08900i
$317$	9.74907	−	9.74907i	0.547562	−	0.547562i	−0.378173	−	0.925735i	$-0.623447\pi$
$317$	9.74907	−	9.74907i	0.547562	−	0.547562i	0.925735	+	0.378173i	$0.123447\pi$
$318$	2.44014	−	6.25586i	0.136836	−	0.350811i
$319$	−5.94796			−0.333022
$320$	−3.48035	−	17.5467i	−0.194558	−	0.980891i
$321$	−3.98902			−0.222645
$322$	0.357189	−	0.915735i	0.0199053	−	0.0510319i
$323$	2.67962	−	2.67962i	0.149098	−	0.149098i
$324$	−4.73257	−	4.35445i	−0.262921	−	0.241914i
$325$	2.00694	−	2.67698i	0.111325	−	0.148492i
$326$	−5.11999	−	11.6684i	−0.283570	−	0.646254i
$327$	−8.67936	−	8.67936i	−0.479970	−	0.479970i
$328$	13.0573	−	6.38941i	0.720968	−	0.352796i
$329$			1.03159i			0.0568734i
$330$	1.20939	−	3.89772i	0.0665746	−	0.214563i
$331$			10.2373i			0.562695i	0.959606	+	0.281348i	$0.0907814\pi$
$331$			10.2373i			0.562695i	−0.959606	+	0.281348i	$0.909219\pi$
$332$	33.6745	−	1.40125i	1.84813	−	0.0769036i
$333$	−7.03362	−	7.03362i	−0.385440	−	0.385440i
$334$	21.9843	−	9.64650i	1.20293	−	0.527833i
$335$	−17.2711	+	1.22906i	−0.943619	+	0.0671509i
$336$	0.0396093	+	0.475116i	0.00216087	+	0.0259197i
$337$	15.6491	−	15.6491i	0.852460	−	0.852460i	−0.137976	−	0.990436i	$-0.544060\pi$
$337$	15.6491	−	15.6491i	0.852460	−	0.852460i	0.990436	+	0.137976i	$0.0440596\pi$
$338$	−16.5380	−	6.45075i	−0.899548	−	0.350875i
$339$	−20.2161			−1.09799
$340$	3.98376	−	4.99990i	0.216050	−	0.271157i
$341$	1.44287			0.0781356
$342$	−4.66111	−	1.81810i	−0.252044	−	0.0983114i
$343$	0.913738	−	0.913738i	0.0493372	−	0.0493372i
$344$	−5.26859	+	15.3657i	−0.284063	+	0.828463i
$345$	−16.4072	−	14.2271i	−0.883333	−	0.765964i
$346$	−10.1894	+	4.47100i	−0.547784	+	0.240362i
$347$	−15.8467	−	15.8467i	−0.850698	−	0.850698i	0.139521	−	0.990219i	$-0.455444\pi$
$347$	−15.8467	−	15.8467i	−0.850698	−	0.850698i	−0.990219	+	0.139521i	$0.955444\pi$
$348$	−0.638275	−	15.3389i	−0.0342151	−	0.822249i
$349$		−	22.8492i		−	1.22309i	−0.791209	−	0.611545i	$-0.790548\pi$
$349$		−	22.8492i		−	1.22309i	0.791209	−	0.611545i	$-0.209452\pi$
$350$	−0.344452	−	0.554843i	−0.0184117	−	0.0296576i
$351$			3.74313i			0.199793i
$352$	−1.61070	+	5.42270i	−0.0858508	+	0.289031i
$353$	1.30502	+	1.30502i	0.0694591	+	0.0694591i	0.740983	−	0.671524i	$-0.234360\pi$
$353$	1.30502	+	1.30502i	0.0694591	+	0.0694591i	−0.671524	+	0.740983i	$0.734360\pi$
$354$	5.64863	+	12.8732i	0.300221	+	0.684202i
$355$	3.04227	+	2.63804i	0.161467	+	0.140013i
$356$	−7.71448	+	8.38438i	−0.408867	+	0.444371i
$357$	−0.120479	+	0.120479i	−0.00637644	+	0.00637644i
$358$	2.13503	−	5.47364i	0.112840	−	0.289291i
$359$	4.81259			0.253999			0.127000	−	0.991903i	$-0.459465\pi$
$359$	4.81259			0.253999			0.127000	+	0.991903i	$0.459465\pi$
$360$	−8.15811	−	2.16389i	−0.429970	−	0.114047i
$361$	−11.9724			−0.630125
$362$	−4.86517	+	12.4730i	−0.255708	+	0.655566i
$363$	−0.912547	+	0.912547i	−0.0478963	+	0.0478963i
$364$	0.0836909	−	0.0909583i	0.00438659	−	0.00476751i
$365$	16.2894	−	1.15920i	0.852626	−	0.0606755i
$366$	−5.18410	−	11.8145i	−0.270977	−	0.617556i
$367$	−9.09859	−	9.09859i	−0.474942	−	0.474942i	0.428567	−	0.903510i	$-0.359018\pi$
$367$	−9.09859	−	9.09859i	−0.474942	−	0.474942i	−0.903510	+	0.428567i	$0.859018\pi$
$368$	22.9801	+	19.4433i	1.19792	+	1.01355i
$369$		−	6.85876i		−	0.357053i
$370$	22.5118	+	6.98499i	1.17033	+	0.363132i
$371$			0.339804i			0.0176418i
$372$	0.154834	+	3.72093i	0.00802776	+	0.192921i
$373$	−5.77605	−	5.77605i	−0.299073	−	0.299073i	0.541578	−	0.840651i	$-0.317827\pi$
$373$	−5.77605	−	5.77605i	−0.299073	−	0.299073i	−0.840651	+	0.541578i	$0.817827\pi$
$374$	−1.85124	+	0.812306i	−0.0957253	+	0.0420033i
$375$	−14.1022	+	3.05195i	−0.728233	+	0.157602i
$376$	−29.8842	−	10.2467i	−1.54116	−	0.528433i
$377$	−2.81434	+	2.81434i	−0.144946	+	0.144946i
$378$	0.680685	+	0.265506i	0.0350106	+	0.0136561i
$379$	21.9568			1.12784			0.563922	−	0.825828i	$-0.309292\pi$
$379$	21.9568			1.12784			0.563922	+	0.825828i	$0.309292\pi$
$380$	11.7804	−	1.33247i	0.604320	−	0.0683545i
$381$	5.07207			0.259850
$382$	24.5634	+	9.58112i	1.25677	+	0.490213i
$383$	−5.58752	+	5.58752i	−0.285509	+	0.285509i	−0.835301	−	0.549792i	$-0.814707\pi$
$383$	−5.58752	+	5.58752i	−0.285509	+	0.285509i	0.549792	+	0.835301i	$0.314707\pi$
$384$	−14.1571	−	3.57184i	−0.722453	−	0.182275i
$385$	0.0146594	+	0.205997i	0.000747113	+	0.0104986i
$386$	35.6738	−	15.6533i	1.81575	−	0.796733i
$387$	5.41942	+	5.41942i	0.275484	+	0.275484i
$388$	1.12579	−	0.0468459i	0.0571532	−	0.00237824i
$389$			20.2159i			1.02498i	0.858692	+	0.512492i	$0.171278\pi$
$389$			20.2159i			1.02498i	−0.858692	+	0.512492i	$0.828722\pi$
$390$	−1.27201	−	2.41648i	−0.0644109	−	0.122363i
$391$			10.7577i			0.544039i
$392$	8.69174	+	17.7623i	0.438999	+	0.897131i
$393$	5.31152	+	5.31152i	0.267931	+	0.267931i
$394$	−11.0396	−	25.1591i	−0.556166	−	1.26750i
$395$	−20.9412	+	24.1501i	−1.05367	+	1.21512i
$396$	1.96412	+	1.80719i	0.0987009	+	0.0908148i
$397$	−15.6155	+	15.6155i	−0.783719	+	0.783719i	−0.980456	−	0.196737i	$-0.936965\pi$
$397$	−15.6155	+	15.6155i	−0.783719	+	0.783719i	0.196737	+	0.980456i	$0.436965\pi$
$398$	4.81129	−	12.3349i	0.241168	−	0.618291i
$399$	−0.315972			−0.0158184
$400$	19.4947	−	4.46724i	0.974736	−	0.223362i
$401$	1.85459			0.0926139			0.0463070	−	0.998927i	$-0.485255\pi$
$401$	1.85459			0.0926139			0.0463070	+	0.998927i	$0.485255\pi$
$402$	−5.13559	+	13.1663i	−0.256140	+	0.656674i
$403$	0.682708	−	0.682708i	0.0340081	−	0.0340081i
$404$	16.5680	+	15.2442i	0.824287	+	0.758428i
$405$	4.71047	−	5.43226i	0.234065	−	0.269931i
$406$	0.312160	+	0.711411i	0.0154923	+	0.0353067i
$407$	−5.27054	−	5.27054i	−0.261251	−	0.261251i
$408$	−2.29346	−	4.68689i	−0.113543	−	0.232035i
$409$			0.431928i			0.0213575i	0.999943	+	0.0106787i	$0.00339921\pi$
$409$			0.431928i			0.0213575i	−0.999943	+	0.0106787i	$0.996601\pi$
$410$	7.57042	+	14.3818i	0.373877	+	0.710265i
$411$			9.05673i			0.446736i
$412$	−13.7740	+	0.573159i	−0.678596	+	0.0282375i
$413$	−0.503031	−	0.503031i	−0.0247525	−	0.0247525i
$414$	13.0058	−	5.70682i	0.639200	−	0.280475i
$415$	2.67479	+	37.5868i	0.131300	+	1.84506i
$416$	1.80369	+	3.32793i	0.0884329	+	0.163165i
$417$	−17.9191	+	17.9191i	−0.877500	+	0.877500i
$418$	−3.49274	−	1.36237i	−0.170835	−	0.0666355i
$419$	35.1667			1.71801			0.859003	−	0.511971i	$-0.171084\pi$
$419$	35.1667			1.71801			0.859003	+	0.511971i	$0.171084\pi$
$420$	−0.529661	+	0.0599099i	−0.0258448	+	0.00292330i
$421$	22.8147			1.11192			0.555959	−	0.831210i	$-0.312351\pi$
$421$	22.8147			1.11192			0.555959	+	0.831210i	$0.312351\pi$
$422$	−25.1626	−	9.81485i	−1.22490	−	0.477779i
$423$	−10.5400	+	10.5400i	−0.512474	+	0.512474i
$424$	−9.84382	−	3.37525i	−0.478058	−	0.163916i
$425$	5.71881	+	4.28741i	0.277403	+	0.207970i
$426$	3.00967	−	1.32061i	0.145819	−	0.0639839i
$427$	0.461664	+	0.461664i	0.0223415	+	0.0223415i
$428$	0.257019	+	6.17660i	0.0124235	+	0.298557i
$429$			0.863563i			0.0416932i
$430$	−17.3454	−	5.38195i	−0.836470	−	0.259541i
$431$		−	30.3483i		−	1.46183i	−0.682470	−	0.730914i	$-0.739094\pi$
$431$		−	30.3483i		−	1.46183i	0.682470	−	0.730914i	$-0.260906\pi$
$432$	−14.4526	+	17.0816i	−0.695353	+	0.821837i
$433$	−11.3120	−	11.3120i	−0.543619	−	0.543619i	0.380969	−	0.924588i	$-0.375591\pi$
$433$	−11.3120	−	11.3120i	−0.543619	−	0.543619i	−0.924588	+	0.380969i	$0.875591\pi$
$434$	−0.0757244	−	0.172575i	−0.00363489	−	0.00828389i
$435$	17.1209	−	1.21838i	0.820884	−	0.0584167i
$436$	−12.8799	+	13.9984i	−0.616836	+	0.670400i
$437$	−14.1067	+	14.1067i	−0.674813	+	0.674813i
$438$	4.84369	−	12.4179i	0.231441	−	0.593351i
$439$	−38.9791			−1.86037			−0.930186	−	0.367089i	$-0.880354\pi$
$439$	−38.9791			−1.86037			−0.930186	+	0.367089i	$0.880354\pi$
$440$	−6.11317	−	1.62148i	−0.291434	−	0.0773012i
$441$	9.33022			0.444296
$442$	−0.491583	+	1.26029i	−0.0233822	+	0.0599457i
$443$	−15.0112	+	15.0112i	−0.713203	+	0.713203i	−0.967204	−	0.254001i	$-0.918253\pi$
$443$	−15.0112	+	15.0112i	−0.713203	+	0.713203i	0.254001	+	0.967204i	$0.418253\pi$
$444$	13.0263	−	14.1575i	0.618202	−	0.671884i
$445$	−9.62398	−	8.34523i	−0.456220	−	0.395602i
$446$	−1.22902	−	2.80093i	−0.0581958	−	0.132628i
$447$	21.2443	+	21.2443i	1.00482	+	1.00482i
$448$	0.733119	−	0.0919437i	0.0346366	−	0.00434393i
$449$			34.7687i			1.64084i	0.571763	+	0.820419i	$0.306260\pi$
$449$			34.7687i			1.64084i	−0.571763	+	0.820419i	$0.693740\pi$
$450$	2.14963	−	9.18834i	0.101335	−	0.433142i
$451$		−	5.13952i		−	0.242011i
$452$	1.30256	+	31.3027i	0.0612671	+	1.47235i
$453$	−7.03430	−	7.03430i	−0.330500	−	0.330500i
$454$	−13.7472	+	6.03214i	−0.645188	+	0.283102i
$455$	0.104406	+	0.0905336i	0.00489463	+	0.00424428i
$456$	3.13852	−	9.15341i	0.146975	−	0.428648i
$457$	6.92112	−	6.92112i	0.323756	−	0.323756i	−0.526450	−	0.850206i	$-0.676477\pi$
$457$	6.92112	−	6.92112i	0.323756	−	0.323756i	0.850206	+	0.526450i	$0.176477\pi$
$458$	17.5949	+	6.86301i	0.822156	+	0.320687i
$459$	−7.99640			−0.373240
$460$	−20.9722	+	26.3216i	−0.977834	+	1.22725i
$461$	3.63769			0.169424			0.0847120	−	0.996405i	$-0.473003\pi$
$461$	3.63769			0.169424			0.0847120	+	0.996405i	$0.473003\pi$
$462$	0.157038	+	0.0612538i	0.00730608	+	0.00284979i
$463$	−7.52465	+	7.52465i	−0.349700	+	0.349700i	−0.859998	−	0.510298i	$-0.829535\pi$
$463$	−7.52465	+	7.52465i	−0.349700	+	0.349700i	0.510298	+	0.859998i	$0.329535\pi$
$464$	−23.7096	+	1.97661i	−1.10069	+	0.0917620i
$465$	−4.15322	+	0.295556i	−0.192601	+	0.0137061i
$466$	7.91541	−	3.47320i	0.366674	−	0.160893i
$467$	−2.70144	−	2.70144i	−0.125008	−	0.125008i	0.641835	−	0.766843i	$-0.278173\pi$
$467$	−2.70144	−	2.70144i	−0.125008	−	0.125008i	−0.766843	+	0.641835i	$0.778173\pi$
$468$	1.78444	−	0.0742534i	0.0824857	−	0.00343237i
$469$		−	0.715162i		−	0.0330231i
$470$	10.4672	−	33.7345i	0.482814	−	1.55606i
$471$		−	23.6842i		−	1.09131i
$472$	19.5689	−	9.57579i	0.900732	−	0.440761i
$473$	4.06096	+	4.06096i	0.186723	+	0.186723i
$474$	10.4833	+	23.8913i	0.481512	+	1.09736i
$475$	1.87701	+	13.1213i	0.0861229	+	0.602045i
$476$	0.194313	+	0.178788i	0.00890633	+	0.00819473i
$477$	−3.47187	+	3.47187i	−0.158966	+	0.158966i
$478$	12.9940	−	33.3132i	0.594334	−	1.52371i
$479$	6.43233			0.293901			0.146950	−	0.989144i	$-0.453054\pi$
$479$	6.43233			0.293901			0.146950	+	0.989144i	$0.453054\pi$
$480$	3.52555	−	15.9389i	0.160918	−	0.727507i
$481$	−4.98763			−0.227416
$482$	−5.65370	+	14.4946i	−0.257519	+	0.660209i
$483$	0.634255	−	0.634255i	0.0288596	−	0.0288596i
$484$	1.47179	+	1.35419i	0.0668994	+	0.0615543i
$485$	0.0894222	+	1.25658i	0.00406045	+	0.0570584i
$486$	7.17796	+	16.3585i	0.325599	+	0.742038i
$487$	10.7615	+	10.7615i	0.487648	+	0.487648i	0.907563	−	0.419915i	$-0.137940\pi$
$487$	10.7615	+	10.7615i	0.487648	+	0.487648i	−0.419915	+	0.907563i	$0.637940\pi$
$488$	−17.9596	+	8.78831i	−0.812995	+	0.397828i
$489$		−	11.6280i		−	0.525834i
$490$	−19.5640	+	10.2983i	−0.883813	+	0.465230i
$491$			17.1022i			0.771810i	0.922538	+	0.385905i	$0.126111\pi$
$491$			17.1022i			0.771810i	−0.922538	+	0.385905i	$0.873889\pi$
$492$	13.2540	−	0.551521i	0.597537	−	0.0248645i
$493$	−6.01225	−	6.01225i	−0.270778	−	0.270778i
$494$	−2.29724	+	1.00801i	−0.103358	+	0.0453524i
$495$	−1.95495	+	2.25451i	−0.0878685	+	0.101333i
$496$	5.75152	−	0.479490i	0.258251	−	0.0215298i
$497$	−0.117605	+	0.117605i	−0.00527533	+	0.00527533i
$498$	28.6536	+	11.1765i	1.28400	+	0.500832i
$499$	13.6674			0.611839			0.305919	−	0.952057i	$-0.401036\pi$
$499$	13.6674			0.611839			0.305919	+	0.952057i	$0.401036\pi$
$500$	5.63427	+	21.6392i	0.251972	+	0.967734i
$501$	21.9081			0.978780
$502$	38.9533	+	15.1940i	1.73857	+	0.678142i
$503$	26.9531	−	26.9531i	1.20178	−	1.20178i	0.228153	−	0.973625i	$-0.426731\pi$
$503$	26.9531	−	26.9531i	1.20178	−	1.20178i	0.973625	−	0.228153i	$-0.0732686\pi$
$504$	0.113070	−	0.329765i	0.00503653	−	0.0146889i
$505$	−16.4906	+	19.0175i	−0.733822	+	0.846266i
$506$	9.74572	−	4.27633i	0.433250	−	0.190106i
$507$	−11.4545	−	11.4545i	−0.508713	−	0.508713i
$508$	−0.326802	−	7.85361i	−0.0144995	−	0.348448i
$509$			27.2015i			1.20568i	0.797860	+	0.602842i	$0.205965\pi$
$509$			27.2015i			1.20568i	−0.797860	+	0.602842i	$0.794035\pi$
$510$	5.16231	−	2.71739i	0.228591	−	0.120328i
$511$			0.674513i			0.0298387i
$512$	−4.61848	+	22.1511i	−0.204110	+	0.978948i
$513$	−10.4858	−	10.4858i	−0.462958	−	0.462958i
$514$	−9.77172	−	22.2697i	−0.431012	−	0.982274i
$515$	−1.09408	−	15.3742i	−0.0482109	−	0.677470i
$516$	−10.0368	+	10.9084i	−0.441846	+	0.480214i
$517$	−7.89803	+	7.89803i	−0.347355	+	0.347355i
$518$	−0.353780	+	0.906996i	−0.0155442	+	0.0398511i
$519$	−10.1540			−0.445713
$520$	−3.65973	+	2.12529i	−0.160490	+	0.0932000i
$521$	44.8315			1.96411			0.982053	−	0.188607i	$-0.0603971\pi$
$521$	44.8315			1.96411			0.982053	+	0.188607i	$0.0603971\pi$
$522$	−4.07925	+	10.4581i	−0.178544	+	0.457739i
$523$	−12.3555	+	12.3555i	−0.540267	+	0.540267i	−0.923607	−	0.383340i	$-0.874774\pi$
$523$	−12.3555	+	12.3555i	−0.540267	+	0.540267i	0.383340	+	0.923607i	$0.374774\pi$
$524$	7.88214	−	8.56660i	0.344333	−	0.374234i
$525$	−0.0843928	−	0.589950i	−0.00368320	−	0.0257475i
$526$	−10.8674	−	24.7666i	−0.473840	−	1.07988i
$527$	1.45846	+	1.45846i	0.0635316	+	0.0635316i
$528$	−3.33431	+	3.94083i	−0.145107	+	0.171502i
$529$		−	33.6330i		−	1.46230i
$530$	3.44787	−	11.1121i	0.149766	−	0.482678i
$531$		−	10.2792i		−	0.446080i
$532$	0.0203586	+	0.489251i	0.000882655	+	0.0212117i
$533$	−2.43182	−	2.43182i	−0.105334	−	0.105334i
$534$	−9.52084	+	4.17765i	−0.412007	+	0.180785i
$535$	−6.89420	+	0.490613i	−0.298062	+	0.0212110i
$536$	20.7176	+	7.10364i	0.894864	+	0.306831i
$537$	3.79114	−	3.79114i	0.163600	−	0.163600i
$538$	−1.91959	−	0.748748i	−0.0827593	−	0.0322808i
$539$	6.99147			0.301144
$540$	−19.5654	−	15.5891i	−0.841960	−	0.670847i
$541$	−18.6640			−0.802428			−0.401214	−	0.915984i	$-0.631412\pi$
$541$	−18.6640			−0.802428			−0.401214	+	0.915984i	$0.631412\pi$
$542$	−11.2839	−	4.40136i	−0.484685	−	0.189055i
$543$	−8.63902	+	8.63902i	−0.370736	+	0.370736i
$544$	−7.10942	+	3.85319i	−0.304814	+	0.165204i
$545$	−16.0680	−	13.9330i	−0.688276	−	0.596824i
$546$	0.103287	−	0.0453214i	0.00442029	−	0.00193958i
$547$	−1.26900	−	1.26900i	−0.0542585	−	0.0542585i	0.679457	−	0.733715i	$-0.262215\pi$
$547$	−1.26900	−	1.26900i	−0.0542585	−	0.0542585i	−0.733715	+	0.679457i	$0.762215\pi$
$548$	14.0235	−	0.583540i	0.599053	−	0.0249276i
$549$			9.43389i			0.402628i
$550$	1.61079	−	6.88515i	0.0686845	−	0.293584i
$551$		−	15.7678i		−	0.671733i
$552$	12.0738	+	24.6738i	0.513894	+	1.05019i
$553$	−0.933573	−	0.933573i	−0.0396995	−	0.0396995i
$554$	−6.93644	−	15.8081i	−0.294701	−	0.671622i
$555$	16.2506	+	14.0914i	0.689800	+	0.598145i
$556$	28.9005	+	26.5914i	1.22565	+	1.12773i
$557$	19.0631	−	19.0631i	0.807728	−	0.807728i	−0.176562	−	0.984290i	$-0.556497\pi$
$557$	19.0631	−	19.0631i	0.807728	−	0.807728i	0.984290	+	0.176562i	$0.0564975\pi$
$558$	0.989553	−	2.53695i	0.0418911	−	0.107398i
$559$	3.84298			0.162541
$560$	0.126892	+	0.816269i	0.00536215	+	0.0344937i
$561$	−1.84482			−0.0778884
$562$	4.30385	−	11.0339i	0.181547	−	0.465438i
$563$	16.5536	−	16.5536i	0.697652	−	0.697652i	−0.266251	−	0.963904i	$-0.585785\pi$
$563$	16.5536	−	16.5536i	0.697652	−	0.697652i	0.963904	+	0.266251i	$0.0857851\pi$
$564$	−21.2153	−	19.5202i	−0.893325	−	0.821950i
$565$	−34.9394	+	2.48640i	−1.46991	+	0.104604i
$566$	6.35372	+	14.4801i	0.267067	+	0.608643i
$567$	0.209996	+	0.209996i	0.00881899	+	0.00881899i
$568$	−2.23876	−	4.57509i	−0.0939362	−	0.191966i
$569$		−	35.6168i		−	1.49313i	−0.665310	−	0.746567i	$-0.731701\pi$
$569$		−	35.6168i		−	1.49313i	0.665310	−	0.746567i	$-0.268299\pi$
$570$	10.3327	+	3.20605i	0.432790	+	0.134287i
$571$		−	6.36739i		−	0.266467i	−0.991085	−	0.133233i	$-0.957464\pi$
$571$		−	6.36739i		−	0.266467i	0.991085	−	0.133233i	$-0.0425360\pi$
$572$	1.33714	−	0.0556408i	0.0559088	−	0.00232646i
$573$	17.0131	+	17.0131i	0.710730	+	0.710730i
$574$	−0.614717	+	0.269732i	−0.0256578	+	0.0112584i
$575$	−30.1062	−	22.5708i	−1.25552	−	0.941266i
$576$	8.42989	+	6.55106i	0.351245	+	0.272961i
$577$	7.84577	−	7.84577i	0.326624	−	0.326624i	−0.524677	−	0.851301i	$-0.675814\pi$
$577$	7.84577	−	7.84577i	0.326624	−	0.326624i	0.851301	+	0.524677i	$0.175814\pi$
$578$	19.7057	+	7.68635i	0.819650	+	0.319710i
$579$	35.5501			1.47741
$580$	−2.98967	−	26.4315i	−0.124139	−	1.09751i
$581$	−1.55640			−0.0645702
$582$	0.957931	+	0.373647i	0.0397075	+	0.0154882i
$583$	−2.60160	+	2.60160i	−0.107747	+	0.107747i
$584$	−19.5400	−	6.69988i	−0.808572	−	0.277243i
$585$	0.141739	+	1.99175i	0.00586020	+	0.0823488i
$586$	−14.5478	+	6.38344i	−0.600965	+	0.263698i
$587$	−5.28478	−	5.28478i	−0.218126	−	0.218126i	0.589582	−	0.807708i	$-0.299292\pi$
$587$	−5.28478	−	5.28478i	−0.218126	−	0.218126i	−0.807708	+	0.589582i	$0.799292\pi$
$588$	0.750254	+	18.0299i	0.0309399	+	0.743540i
$589$			3.82499i			0.157606i
$590$	11.3458	+	21.5539i	0.467098	+	0.887361i
$591$		−	25.0719i		−	1.03132i
$592$	−22.7608	−	19.2578i	−0.935462	−	0.791490i
$593$	18.6597	+	18.6597i	0.766261	+	0.766261i	0.977446	−	0.211185i	$-0.0677323\pi$
$593$	18.6597	+	18.6597i	0.766261	+	0.766261i	−0.211185	+	0.977446i	$0.567732\pi$
$594$	3.17868	+	7.24419i	0.130423	+	0.297233i
$595$	−0.193406	+	0.223042i	−0.00792887	+	0.00914381i
$596$	31.5260	−	34.2636i	1.29135	−	1.40349i
$597$	8.54335	−	8.54335i	0.349656	−	0.349656i
$598$	2.58790	−	6.63468i	0.105827	−	0.271312i
$599$	3.72864			0.152348			0.0761740	−	0.997095i	$-0.475730\pi$
$599$	3.72864			0.152348			0.0761740	+	0.997095i	$0.475730\pi$
$600$	17.9286	+	3.41514i	0.731931	+	0.139423i
$601$	13.4770			0.549738			0.274869	−	0.961482i	$-0.411366\pi$
$601$	13.4770			0.549738			0.274869	+	0.961482i	$0.411366\pi$
$602$	0.272588	−	0.698842i	0.0111099	−	0.0284827i
$603$	7.30701	−	7.30701i	0.297564	−	0.297564i
$604$	−10.4387	+	11.3452i	−0.424745	+	0.461628i
$605$	−1.46492	+	1.68939i	−0.0595573	+	0.0686833i
$606$	8.25526	+	18.8137i	0.335347	+	0.764253i
$607$	6.89298	+	6.89298i	0.279778	+	0.279778i	0.833020	−	0.553243i	$-0.186610\pi$
$607$	6.89298	+	6.89298i	0.279778	+	0.279778i	−0.553243	+	0.833020i	$0.686610\pi$
$608$	−14.3754	−	4.26992i	−0.582999	−	0.173168i
$609$			0.708944i			0.0287279i
$610$	−10.4127	−	19.7814i	−0.421599	−	0.800926i
$611$			7.47407i			0.302369i
$612$	0.158627	+	3.81207i	0.00641210	+	0.154094i
$613$	27.1964	+	27.1964i	1.09845	+	1.09845i	0.994592	+	0.103862i	$0.0331201\pi$
$613$	27.1964	+	27.1964i	1.09845	+	1.09845i	0.103862	+	0.994592i	$0.466880\pi$
$614$	−24.5057	+	10.7529i	−0.988969	+	0.433950i
$615$	1.05278	+	14.7938i	0.0424520	+	0.596545i
$616$	0.0847274	−	0.247105i	0.00341376	−	0.00995615i
$617$	−21.2184	+	21.2184i	−0.854219	+	0.854219i	−0.990650	−	0.136431i	$-0.956437\pi$
$617$	−21.2184	+	21.2184i	−0.854219	+	0.854219i	0.136431	+	0.990650i	$0.456437\pi$
$618$	−11.7203	−	4.57157i	−0.471459	−	0.183896i
$619$	−17.1338			−0.688664			−0.344332	−	0.938848i	$-0.611895\pi$
$619$	−17.1338			−0.688664			−0.344332	+	0.938848i	$0.611895\pi$
$620$	0.725239	+	6.41181i	0.0291263	+	0.257505i
$621$	42.0965			1.68927
$622$	−42.8481	−	16.7132i	−1.71805	−	0.670137i
$623$	0.372035	−	0.372035i	0.0149053	−	0.0149053i
$624$	0.286977	+	3.44231i	0.0114883	+	0.137803i
$625$	−23.9973	+	7.00911i	−0.959894	+	0.280364i
$626$	−27.2870	+	11.9733i	−1.09061	+	0.478548i
$627$	−2.41913	−	2.41913i	−0.0966108	−	0.0966108i
$628$	−36.6726	+	1.52601i	−1.46340	+	0.0608944i
$629$		−	10.6550i		−	0.424843i
$630$	0.372252	+	0.115503i	0.0148309	+	0.00460174i
$631$		−	8.57760i		−	0.341469i	−0.985317	−	0.170734i	$-0.945386\pi$
$631$		−	8.57760i		−	0.341469i	0.985317	−	0.170734i	$-0.0546140\pi$
$632$	36.3178	−	17.7716i	1.44465	−	0.706918i
$633$	−17.4281	−	17.4281i	−0.692704	−	0.692704i
$634$	−7.83455	−	17.8549i	−0.311150	−	0.709108i
$635$	8.76604	−	0.623819i	0.347870	−	0.0247555i
$636$	−6.98829	−	6.42994i	−0.277104	−	0.254964i
$637$	3.30809	−	3.30809i	0.131071	−	0.131071i
$638$	−3.05673	+	7.83664i	−0.121017	+	0.310255i
$639$	−2.40321			−0.0950697
$640$	−24.9070	−	4.43200i	−0.984535	−	0.175190i
$641$	−16.8822			−0.666806			−0.333403	−	0.942784i	$-0.608197\pi$
$641$	−16.8822			−0.666806			−0.333403	+	0.942784i	$0.608197\pi$
$642$	−2.05001	+	5.25566i	−0.0809073	+	0.207424i
$643$	13.6321	−	13.6321i	0.537596	−	0.537596i	−0.385226	−	0.922822i	$-0.625877\pi$
$643$	13.6321	−	13.6321i	0.537596	−	0.537596i	0.922822	+	0.385226i	$0.125877\pi$
$644$	−1.02295	−	0.941216i	−0.0403098	−	0.0370891i
$645$	−12.5211	−	10.8574i	−0.493019	−	0.427511i
$646$	−2.15340	−	4.90757i	−0.0847242	−	0.193086i
$647$	−7.57737	−	7.57737i	−0.297897	−	0.297897i	0.542293	−	0.840190i	$-0.317556\pi$
$647$	−7.57737	−	7.57737i	−0.297897	−	0.297897i	−0.840190	+	0.542293i	$0.817556\pi$
$648$	−8.16926	+	3.99752i	−0.320919	+	0.157037i
$649$		−	7.70258i		−	0.302353i
$650$	−2.49562	−	4.01995i	−0.0978863	−	0.157675i
$651$		−	0.171977i		−	0.00674031i
$652$	−18.0048	+	0.749207i	−0.705120	+	0.0293412i
$653$	17.3117	+	17.3117i	0.677460	+	0.677460i	0.959425	−	0.281964i	$-0.0909860\pi$
$653$	17.3117	+	17.3117i	0.677460	+	0.677460i	−0.281964	+	0.959425i	$0.590986\pi$
$654$	−15.8958	+	6.97491i	−0.621574	+	0.272741i
$655$	9.83314	+	8.52660i	0.384212	+	0.333162i
$656$	−1.70795	−	20.4870i	−0.0666844	−	0.799883i
$657$	−6.89168	+	6.89168i	−0.268870	+	0.268870i
$658$	1.35915	+	0.530147i	0.0529853	+	0.0206673i
$659$	13.6092			0.530139			0.265070	−	0.964229i	$-0.414605\pi$
$659$	13.6092			0.530139			0.265070	+	0.964229i	$0.414605\pi$
$660$	−4.51386	−	3.59650i	−0.175702	−	0.139993i
$661$	−18.6616			−0.725854			−0.362927	−	0.931818i	$-0.618223\pi$
$661$	−18.6616			−0.725854			−0.362927	+	0.931818i	$0.618223\pi$
$662$	13.4880	+	5.26110i	0.524228	+	0.204479i
$663$	−0.872896	+	0.872896i	−0.0339005	+	0.0339005i
$664$	15.4595	−	45.0874i	0.599947	−	1.74973i
$665$	−0.546092	+	0.0388616i	−0.0211765	+	0.00150699i
$666$	−12.8817	+	5.65236i	−0.499155	+	0.219024i
$667$	31.6510	+	31.6510i	1.22553	+	1.22553i
$668$	−1.41157	−	33.9225i	−0.0546153	−	1.31250i
$669$		−	2.79122i		−	0.107915i
$670$	−7.25649	+	23.3868i	−0.280343	+	0.903512i
$671$			7.06915i			0.272902i
$672$	0.646337	+	0.191982i	0.0249330	+	0.00740585i
$673$	5.01293	+	5.01293i	0.193234	+	0.193234i	0.797092	−	0.603858i	$-0.206370\pi$
$673$	5.01293	+	5.01293i	0.193234	+	0.193234i	−0.603858	+	0.797092i	$0.706370\pi$
$674$	−12.5759	−	28.6605i	−0.484407	−	1.10396i
$675$	16.7773	−	22.3786i	0.645759	−	0.861352i
$676$	−16.9982	+	18.4742i	−0.653776	+	0.710547i
$677$	−17.2931	+	17.2931i	−0.664628	+	0.664628i	−0.956467	−	0.291839i	$-0.905733\pi$
$677$	−17.2931	+	17.2931i	−0.664628	+	0.664628i	0.291839	+	0.956467i	$0.405733\pi$
$678$	−10.3893	+	26.6354i	−0.398999	+	1.02293i
$679$	−0.0520326			−0.00199683
$680$	−4.54023	−	7.81824i	−0.174110	−	0.299816i
$681$	−13.6995			−0.524967
$682$	0.741508	−	1.90103i	0.0283938	−	0.0727940i
$683$	−14.5193	+	14.5193i	−0.555566	+	0.555566i	−0.928042	−	0.372476i	$-0.878509\pi$
$683$	−14.5193	+	14.5193i	−0.555566	+	0.555566i	0.372476	+	0.928042i	$0.378509\pi$
$684$	−4.79080	+	5.20682i	−0.183181	+	0.199088i
$685$	1.11390	+	15.6527i	0.0425597	+	0.598059i
$686$	−0.734299	−	1.67346i	−0.0280357	−	0.0638931i
$687$	12.1865	+	12.1865i	0.464946	+	0.464946i
$688$	17.5372	+	14.8382i	0.668601	+	0.565700i
$689$			2.46195i			0.0937928i
$690$	−27.1766	+	14.3055i	−1.03460	+	0.544601i
$691$		−	39.3921i		−	1.49855i	−0.662261	−	0.749273i	$-0.730403\pi$
$691$		−	39.3921i		−	1.49855i	0.662261	−	0.749273i	$-0.269597\pi$
$692$	0.654241	+	15.7225i	0.0248705	+	0.597682i
$693$	−0.0871529	−	0.0871529i	−0.00331067	−	0.00331067i
$694$	−29.0225	+	12.7348i	−1.10168	+	0.483405i
$695$	−28.7655	+	33.1733i	−1.09114	+	1.25833i
$696$	−20.5375	−	7.04188i	−0.778471	−	0.266922i
$697$	5.19507	−	5.19507i	0.196777	−	0.196777i
$698$	−30.1046	−	11.7425i	−1.13948	−	0.444460i
$699$	7.88796			0.298350
$700$	−0.908043	+	0.168685i	−0.0343208	+	0.00637571i
$701$	−20.8661			−0.788101			−0.394050	−	0.919089i	$-0.628926\pi$
$701$	−20.8661			−0.788101			−0.394050	+	0.919089i	$0.628926\pi$
$702$	4.93169	+	1.92364i	0.186135	+	0.0726031i
$703$	13.9720	−	13.9720i	0.526965	−	0.526965i
$704$	6.31682	+	4.90895i	0.238074	+	0.185013i
$705$	21.1162	−	24.3519i	0.795283	−	0.917145i
$706$	2.39007	−	1.04874i	0.0899515	−	0.0394698i
$707$	−0.735161	−	0.735161i	−0.0276486	−	0.0276486i
$708$	19.8637	−	0.826563i	0.746525	−	0.0310641i
$709$			8.62821i			0.324039i	0.986788	+	0.162020i	$0.0518008\pi$
$709$			8.62821i			0.324039i	−0.986788	+	0.162020i	$0.948199\pi$
$710$	5.03917	−	2.65257i	0.189117	−	0.0995492i
$711$		−	19.0771i		−	0.715448i
$712$	7.08213	+	14.4729i	0.265414	+	0.542396i
$713$	−7.67797	−	7.67797i	−0.287542	−	0.287542i
$714$	0.0968196	+	0.220651i	0.00362338	+	0.00825767i
$715$	0.106210	+	1.49249i	0.00397204	+	0.0558160i
$716$	−6.11448	−	5.62594i	−0.228509	−	0.210251i
$717$	23.0733	−	23.0733i	0.861689	−	0.861689i
$718$	2.47325	−	6.34075i	0.0923010	−	0.236635i
$719$	−11.5151			−0.429441			−0.214721	−	0.976676i	$-0.568884\pi$
$719$	−11.5151			−0.429441			−0.214721	+	0.976676i	$0.568884\pi$
$720$	−7.04356	+	9.63653i	−0.262498	+	0.359132i
$721$	0.636619			0.0237089
$722$	−6.15276	+	15.7740i	−0.228982	+	0.587048i
$723$	−10.0392	+	10.0392i	−0.373362	+	0.373362i
$724$	13.9333	+	12.8201i	0.517827	+	0.476454i
$725$	29.4401	−	4.21143i	1.09338	−	0.156409i
$726$	0.733342	+	1.67128i	0.0272169	+	0.0620271i
$727$	−5.97431	−	5.97431i	−0.221575	−	0.221575i	0.587586	−	0.809161i	$-0.300078\pi$
$727$	−5.97431	−	5.97431i	−0.221575	−	0.221575i	−0.809161	+	0.587586i	$0.800078\pi$
$728$	−0.0768308	−	0.157010i	−0.00284754	−	0.00581918i
$729$			25.9484i			0.961051i
$730$	6.84403	−	22.0575i	0.253309	−	0.816386i
$731$			8.20971i			0.303647i
$732$	−18.2302	+	0.758590i	−0.673808	+	0.0280383i
$733$	−16.0677	−	16.0677i	−0.593475	−	0.593475i	0.345093	−	0.938568i	$-0.387847\pi$
$733$	−16.0677	−	16.0677i	−0.593475	−	0.593475i	−0.938568	+	0.345093i	$0.887847\pi$
$734$	−16.6636	+	7.31181i	−0.615064	+	0.269884i
$735$	−20.1246	+	1.43213i	−0.742307	+	0.0528249i
$736$	37.4270	−	20.2848i	1.37958	−	0.747709i
$737$	5.47540	−	5.47540i	0.201689	−	0.201689i
$738$	−9.03665	−	3.52481i	−0.332644	−	0.129750i
$739$	33.7237			1.24055			0.620273	−	0.784386i	$-0.287022\pi$
$739$	33.7237			1.24055			0.620273	+	0.784386i	$0.287022\pi$
$740$	20.7721	−	26.0704i	0.763596	−	0.958367i
$741$	−2.28928			−0.0840987
$742$	0.447703	+	0.174630i	0.0164357	+	0.00641086i
$743$	30.4755	−	30.4755i	1.11804	−	1.11804i	0.126010	−	0.992029i	$-0.459783\pi$
$743$	30.4755	−	30.4755i	1.11804	−	1.11804i	0.992029	−	0.126010i	$-0.0402171\pi$
$744$	4.98202	+	1.70823i	0.182650	+	0.0626268i
$745$	39.3293	+	34.1036i	1.44092	+	1.24946i
$746$	−10.5785	+	4.64176i	−0.387307	+	0.169947i
$747$	−15.9021	−	15.9021i	−0.581828	−	0.581828i
$748$	0.118865	+	2.85652i	0.00434612	+	0.104445i
$749$		−	0.285476i		−	0.0104311i
$750$	−3.22624	+	20.1485i	−0.117806	+	0.735720i
$751$			44.0172i			1.60621i	0.595837	+	0.803106i	$0.296821\pi$
$751$			44.0172i			1.60621i	−0.595837	+	0.803106i	$0.703179\pi$
$752$	−28.8582	+	34.1075i	−1.05235	+	1.24377i
$753$	26.9798	+	26.9798i	0.983198	+	0.983198i
$754$	2.26166	+	5.15432i	0.0823649	+	0.187709i
$755$	−13.0225	−	11.2922i	−0.473937	−	0.410965i
$756$	0.699625	−	0.760378i	0.0254451	−	0.0276547i
$757$	17.1427	−	17.1427i	0.623063	−	0.623063i	−0.323251	−	0.946313i	$-0.604776\pi$
$757$	17.1427	−	17.1427i	0.623063	−	0.623063i	0.946313	+	0.323251i	$0.104776\pi$
$758$	11.2839	−	28.9288i	0.409849	−	1.05074i
$759$	9.71192			0.352520
$760$	4.29850	−	16.2058i	0.155923	−	0.587846i
$761$	−13.6856			−0.496104			−0.248052	−	0.968747i	$-0.579790\pi$
$761$	−13.6856			−0.496104			−0.248052	+	0.968747i	$0.579790\pi$
$762$	2.60660	−	6.68263i	0.0944273	−	0.242086i
$763$	0.621142	−	0.621142i	0.0224868	−	0.0224868i
$764$	25.2469	−	27.4392i	0.913400	−	0.992717i
$765$	−4.25496	+	0.302796i	−0.153838	+	0.0109476i
$766$	4.49025	+	10.2332i	0.162239	+	0.369742i
$767$	−3.64456	−	3.64456i	−0.131597	−	0.131597i
$768$	−11.9815	+	16.8169i	−0.432347	+	0.606826i
$769$			16.3426i			0.589329i	0.955601	+	0.294664i	$0.0952079\pi$
$769$			16.3426i			0.589329i	−0.955601	+	0.294664i	$0.904792\pi$
$770$	0.278942	+	0.0865504i	0.0100524	+	0.00311906i
$771$		−	22.1925i		−	0.799242i
$772$	−2.29055	−	55.0459i	−0.0824387	−	1.98114i
$773$	13.7493	+	13.7493i	0.494529	+	0.494529i	0.909730	−	0.415201i	$-0.136289\pi$
$773$	13.7493	+	13.7493i	0.494529	+	0.494529i	−0.415201	+	0.909730i	$0.636289\pi$
$774$	9.92537	−	4.35515i	0.356760	−	0.156543i
$775$	−7.14163	+	1.02162i	−0.256535	+	0.0366975i
$776$	0.516835	−	1.50734i	0.0185533	−	0.0541103i
$777$	−0.628202	+	0.628202i	−0.0225366	+	0.0225366i
$778$	26.6351	+	10.3892i	0.954913	+	0.372470i
$779$	13.6247			0.488155
$780$	−3.83750	+	0.434059i	−0.137405	+	0.0155418i
$781$	−1.80081			−0.0644382
$782$	14.1736	+	5.52850i	0.506847	+	0.197699i
$783$	−23.5269	+	23.5269i	−0.840781	+	0.840781i
$784$	27.8692	−	2.32339i	0.995329	−	0.0829782i
$785$	−2.91294	−	40.9332i	−0.103967	−	1.46097i
$786$	9.72776	−	4.26845i	0.346978	−	0.152250i
$787$	−4.58243	−	4.58243i	−0.163346	−	0.163346i	0.620701	−	0.784047i	$-0.286848\pi$
$787$	−4.58243	−	4.58243i	−0.163346	−	0.163346i	−0.784047	+	0.620701i	$0.786848\pi$
$788$	−38.8214	+	1.61542i	−1.38295	+	0.0575470i
$789$		−	24.6808i		−	0.878658i
$790$	21.0566	+	40.0018i	0.749159	+	1.42320i
$791$		−	1.44677i		−	0.0514414i
$792$	3.39042	−	1.65906i	0.120473	−	0.0589521i
$793$	3.34485	+	3.34485i	0.118779	+	0.118779i
$794$	12.5489	+	28.5989i	0.445345	+	1.01494i
$795$	6.95566	−	8.02148i	0.246692	−	0.284493i
$796$	−13.7790	−	12.6781i	−0.488384	−	0.449363i
$797$	−21.2355	+	21.2355i	−0.752199	+	0.752199i	−0.974889	−	0.222690i	$-0.928516\pi$
$797$	−21.2355	+	21.2355i	−0.752199	+	0.752199i	0.222690	+	0.974889i	$0.428516\pi$
$798$	−0.162382	+	0.416303i	−0.00574825	+	0.0147370i
$799$	−15.9668			−0.564864
$800$	4.13285	−	27.9807i	0.146118	−	0.989267i
$801$	7.60237			0.268617
$802$	0.953098	−	2.44349i	0.0336551	−	0.0862825i
$803$	−5.16419	+	5.16419i	−0.182240	+	0.182240i
$804$	14.7078	+	13.5326i	0.518703	+	0.477259i
$805$	1.01817	−	1.17419i	0.0358858	−	0.0413846i
$806$	−0.548638	−	1.25034i	−0.0193250	−	0.0440415i
$807$	−1.32954	−	1.32954i	−0.0468021	−	0.0468021i
$808$	28.5992	−	13.9947i	1.00612	−	0.492330i
$809$		−	43.2798i		−	1.52164i	−0.648964	−	0.760819i	$-0.724798\pi$
$809$		−	43.2798i		−	1.52164i	0.648964	−	0.760819i	$-0.275202\pi$
$810$	−4.73641	−	8.99791i	−0.166421	−	0.316154i
$811$			36.0310i			1.26522i	0.774470	+	0.632611i	$0.218017\pi$
$811$			36.0310i			1.26522i	−0.774470	+	0.632611i	$0.781983\pi$
$812$	1.09773	−	0.0456784i	0.0385228	−	0.00160300i
$813$	−7.81544	−	7.81544i	−0.274099	−	0.274099i
$814$	−9.65271	+	4.23552i	−0.338327	+	0.148455i
$815$	−1.43013	−	20.0965i	−0.0500953	−	0.703950i
$816$	−7.35377	+	0.613066i	−0.257433	+	0.0214616i
$817$	−10.7655	+	10.7655i	−0.376636	+	0.376636i
$818$	0.569080	+	0.221973i	0.0198974	+	0.00776111i
$819$	−0.0824747			−0.00288190
$820$	22.8390	−	2.58331i	0.797572	−	0.0902132i
$821$	3.91178			0.136522			0.0682610	−	0.997667i	$-0.478255\pi$
$821$	3.91178			0.136522			0.0682610	+	0.997667i	$0.478255\pi$
$822$	11.9325	+	4.65437i	0.416195	+	0.162340i
$823$	17.9254	−	17.9254i	0.624840	−	0.624840i	−0.321925	−	0.946765i	$-0.604330\pi$
$823$	17.9254	−	17.9254i	0.624840	−	0.624840i	0.946765	+	0.321925i	$0.104330\pi$
$824$	−6.32348	+	18.4423i	−0.220289	+	0.642466i
$825$	3.87063	−	5.16288i	0.134758	−	0.179748i
$826$	−0.921274	+	0.404246i	−0.0320552	+	0.0140655i
$827$	1.97704	+	1.97704i	0.0687485	+	0.0687485i	0.740645	−	0.671897i	$-0.234520\pi$
$827$	1.97704	+	1.97704i	0.0687485	+	0.0687485i	−0.671897	+	0.740645i	$0.734520\pi$
$828$	−0.835079	−	20.0684i	−0.0290210	−	0.697425i
$829$			45.4079i			1.57708i	0.614983	+	0.788540i	$0.289163\pi$
$829$			45.4079i			1.57708i	−0.614983	+	0.788540i	$0.710837\pi$
$830$	50.8964	+	15.7922i	1.76664	+	0.548155i
$831$		−	15.7533i		−	0.546475i
$832$	5.31159	−	0.666150i	0.184146	−	0.0230946i
$833$	7.06703	+	7.06703i	0.244858	+	0.244858i
$834$	14.4001	+	32.8178i	0.498636	+	1.13639i
$835$	37.8636	−	2.69449i	1.31032	−	0.0932467i
$836$	−3.58992	+	3.90166i	−0.124160	+	0.134942i
$837$	5.70719	−	5.70719i	0.197269	−	0.197269i
$838$	18.0726	−	46.3333i	0.624308	−	1.60056i
$839$	−34.1689			−1.17964			−0.589822	−	0.807534i	$-0.700802\pi$
$839$	−34.1689			−1.17964			−0.589822	+	0.807534i	$0.700802\pi$
$840$	−0.193266	+	0.728635i	−0.00666833	+	0.0251403i
$841$	−6.37824			−0.219939
$842$	11.7247	−	30.0591i	0.404061	−	1.03590i
$843$	7.64229	−	7.64229i	0.263215	−	0.263215i
$844$	−25.8628	+	28.1086i	−0.890234	+	0.967539i
$845$	−21.2056	−	18.3880i	−0.729494	−	0.632565i
$846$	8.47019	+	19.3035i	0.291211	+	0.663668i
$847$	−0.0653068	−	0.0653068i	−0.00224397	−	0.00224397i
$848$	−9.50586	+	11.2350i	−0.326433	+	0.385811i
$849$			14.4299i			0.495232i
$850$	8.58777	−	5.33136i	0.294558	−	0.182864i
$851$			56.0925i			1.92283i
$852$	−0.193245	−	4.64402i	−0.00662047	−	0.159101i
$853$	10.3398	+	10.3398i	0.354027	+	0.354027i	0.861606	−	0.507578i	$-0.169459\pi$
$853$	10.3398	+	10.3398i	0.354027	+	0.354027i	−0.507578	+	0.861606i	$0.669459\pi$
$854$	0.845512	−	0.371002i	0.0289328	−	0.0126954i
$855$	−5.97663	−	5.18251i	−0.204396	−	0.177238i
$856$	8.26997	+	2.83560i	0.282662	+	0.0969190i
$857$	23.1527	−	23.1527i	0.790880	−	0.790880i	−0.190758	−	0.981637i	$-0.561094\pi$
$857$	23.1527	−	23.1527i	0.790880	−	0.790880i	0.981637	+	0.190758i	$0.0610944\pi$
$858$	1.13777	+	0.443796i	0.0388429	+	0.0151509i
$859$	19.8852			0.678473			0.339237	−	0.940701i	$-0.389831\pi$
$859$	19.8852			0.678473			0.339237	+	0.940701i	$0.389831\pi$
$860$	−16.0049	+	20.0873i	−0.545763	+	0.684971i
$861$	−0.612585			−0.0208768
$862$	−39.9849	−	15.5964i	−1.36189	−	0.531215i
$863$	−17.7638	+	17.7638i	−0.604686	+	0.604686i	−0.941553	−	0.336866i	$-0.890633\pi$
$863$	−17.7638	+	17.7638i	−0.604686	+	0.604686i	0.336866	+	0.941553i	$0.390633\pi$
$864$	15.0781	+	27.8203i	0.512969	+	0.946465i
$865$	−17.5492	+	1.24885i	−0.596690	+	0.0424623i
$866$	−20.7173	+	9.09054i	−0.704002	+	0.308909i
$867$	13.6485	+	13.6485i	0.463529	+	0.463529i
$868$	−0.266290	+	0.0110808i	−0.00903846	+	0.000376105i
$869$		−	14.2952i		−	0.484931i
$870$	7.19339	−	23.1835i	0.243879	−	0.785994i
$871$		−	5.18149i		−	0.175568i
$872$	11.8242	+	24.1637i	0.400417	+	0.818285i
$873$	−0.531631	−	0.531631i	−0.0179930	−	0.0179930i
$874$	11.3364	+	25.8356i	0.383459	+	0.873901i
$875$	−0.218414	−	1.00923i	−0.00738374	−	0.0341181i
$876$	−13.8718	−	12.7634i	−0.468684	−	0.431237i
$877$	−26.9817	+	26.9817i	−0.911106	+	0.911106i	−0.996359	−	0.0852533i	$-0.972830\pi$
$877$	−26.9817	+	26.9817i	−0.911106	+	0.911106i	0.0852533	+	0.996359i	$0.472830\pi$
$878$	−20.0319	+	51.3563i	−0.676042	+	1.73319i
$879$	−14.4974			−0.488984
$880$	−5.27799	+	7.22100i	−0.177921	+	0.243420i
$881$	−29.0197			−0.977698			−0.488849	−	0.872368i	$-0.662583\pi$
$881$	−29.0197			−0.977698			−0.488849	+	0.872368i	$0.662583\pi$
$882$	4.79492	−	12.2929i	0.161453	−	0.413923i
$883$	−12.7981	+	12.7981i	−0.430690	+	0.430690i	−0.888863	−	0.458173i	$-0.848504\pi$
$883$	−12.7981	+	12.7981i	−0.430690	+	0.430690i	0.458173	+	0.888863i	$0.348504\pi$
$884$	1.40784	+	1.29535i	0.0473507	+	0.0435674i
$885$	1.57779	+	22.1715i	0.0530369	+	0.745286i
$886$	12.0633	+	27.4922i	0.405274	+	0.923618i
$887$	−5.86669	−	5.86669i	−0.196984	−	0.196984i	0.601722	−	0.798706i	$-0.294482\pi$
$887$	−5.86669	−	5.86669i	−0.196984	−	0.196984i	−0.798706	+	0.601722i	$0.794482\pi$
$888$	−11.9586	−	24.4383i	−0.401303	−	0.820096i
$889$			0.362985i			0.0121741i
$890$	−15.9410	+	8.39119i	−0.534344	+	0.281273i
$891$			3.21553i			0.107724i
$892$	−4.32193	+	0.179843i	−0.144709	+	0.00602157i
$893$	−20.9374	−	20.9374i	−0.700643	−	0.700643i
$894$	38.9079	−	17.0724i	1.30127	−	0.570986i
$895$	6.08593	−	7.01848i	0.203430	−	0.234602i
$896$	0.255620	−	1.01316i	0.00853968	−	0.0338473i
$897$	4.59530	−	4.59530i	0.153433	−	0.153433i
$898$	45.8089	+	17.8681i	1.52866	+	0.596266i
$899$	8.58212			0.286230
$900$	−11.0012	−	7.55421i	−0.366707	−	0.251807i
$901$	−5.25943			−0.175217
$902$	−6.77149	−	2.64126i	−0.225466	−	0.0879445i
$903$	0.484031	−	0.484031i	0.0161075	−	0.0161075i
$904$	41.9117	+	14.3707i	1.39396	+	0.477962i
$905$	−13.8682	+	15.9933i	−0.460996	+	0.531635i
$906$	−12.8829	+	5.65291i	−0.428007	+	0.187805i
$907$	−19.7696	−	19.7696i	−0.656438	−	0.656438i	0.298097	−	0.954535i	$-0.403648\pi$
$907$	−19.7696	−	19.7696i	−0.656438	−	0.656438i	−0.954535	+	0.298097i	$0.903648\pi$
$908$	0.882682	+	21.2124i	0.0292928	+	0.703958i
$909$		−	15.0227i		−	0.498271i
$910$	0.172937	−	0.0910322i	0.00573279	−	0.00301769i
$911$			22.0501i			0.730554i	0.930899	+	0.365277i	$0.119026\pi$
$911$			22.0501i			0.730554i	−0.930899	+	0.365277i	$0.880974\pi$
$912$	−10.4470	−	8.83916i	−0.345935	−	0.292694i
$913$	−11.9160	−	11.9160i	−0.394363	−	0.394363i
$914$	−5.56196	−	12.6757i	−0.183973	−	0.419273i
$915$	−1.44804	−	20.3482i	−0.0478708	−	0.672690i
$916$	18.0845	−	19.6549i	0.597528	−	0.649415i
$917$	−0.380121	+	0.380121i	−0.0125527	+	0.0125527i
$918$	−4.10945	+	10.5355i	−0.135632	+	0.347724i
$919$	−8.22053			−0.271170			−0.135585	−	0.990766i	$-0.543291\pi$
$919$	−8.22053			−0.271170			−0.135585	+	0.990766i	$0.543291\pi$
$920$	23.9017	+	41.1586i	0.788016	+	1.35696i
$921$	−24.4207			−0.804690
$922$	1.86945	−	4.79277i	0.0615672	−	0.157842i
$923$	−0.852075	+	0.852075i	−0.0280464	+	0.0280464i
$924$	0.161408	−	0.175424i	0.00530993	−	0.00577103i
$925$	29.8189	+	22.3554i	0.980440	+	0.735040i
$926$	6.04696	+	13.7810i	0.198716	+	0.452871i
$927$	6.50450	+	6.50450i	0.213636	+	0.213636i
$928$	−9.58041	+	32.2540i	−0.314492	+	1.05879i
$929$			51.6745i			1.69539i	0.530487	+	0.847693i	$0.322009\pi$
$929$			51.6745i			1.69539i	−0.530487	+	0.847693i	$0.677991\pi$
$930$	−1.74499	+	5.62389i	−0.0572204	+	0.184415i
$931$			18.5342i			0.607432i
$932$	−0.508234	−	12.2137i	−0.0166478	−	0.400074i
$933$	−29.6773	−	29.6773i	−0.971592	−	0.971592i
$934$	−4.94755	+	2.17094i	−0.161889	+	0.0710352i
$935$	−3.18839	+	0.226896i	−0.104272	+	0.00742029i
$936$	0.819214	−	2.38922i	0.0267768	−	0.0780940i
$937$	−29.9561	+	29.9561i	−0.978623	+	0.978623i	−0.999776	−	0.0211534i	$-0.993266\pi$
$937$	−29.9561	+	29.9561i	−0.978623	+	0.978623i	0.0211534	+	0.999776i	$0.493266\pi$
$938$	−0.942250	−	0.367531i	−0.0307656	−	0.0120003i
$939$	−27.1924			−0.887389
$940$	−39.0671	−	31.1274i	−1.27423	−	1.01526i
$941$	−54.7464			−1.78468			−0.892340	−	0.451363i	$-0.850938\pi$
$941$	−54.7464			−1.78468			−0.892340	+	0.451363i	$0.850938\pi$
$942$	−31.2047	−	12.1716i	−1.01670	−	0.396572i
$943$	−27.3491	+	27.3491i	−0.890608	+	0.890608i
$944$	−2.55971	−	30.7038i	−0.0833113	−	0.999324i
$945$	0.872797	+	0.756828i	0.0283921	+	0.0246196i
$946$	7.43743	−	3.26347i	0.241812	−	0.106105i
$947$	0.414386	+	0.414386i	0.0134657	+	0.0134657i	0.713808	−	0.700342i	$-0.246969\pi$
$947$	0.414386	+	0.414386i	0.0134657	+	0.0134657i	−0.700342	+	0.713808i	$0.746969\pi$
$948$	36.8650	−	1.53401i	1.19732	−	0.0498225i
$949$			4.88698i			0.158638i
$950$	18.2523	+	4.27016i	0.592183	+	0.138542i
$951$		−	17.7930i		−	0.576977i
$952$	0.335419	−	0.164133i	0.0108710	−	0.00531957i
$953$	−7.83757	−	7.83757i	−0.253884	−	0.253884i	0.568677	−	0.822561i	$-0.307455\pi$
$953$	−7.83757	−	7.83757i	−0.253884	−	0.253884i	−0.822561	+	0.568677i	$0.807455\pi$
$954$	2.79007	+	6.35855i	0.0903318	+	0.205866i
$955$	31.4960	+	27.3111i	1.01919	+	0.883767i
$956$	−37.2135	−	34.2402i	−1.20357	−	1.10741i
$957$	−5.42780	+	5.42780i	−0.175456	+	0.175456i
$958$	3.30566	−	8.47481i	0.106801	−	0.273809i
$959$	−0.648149			−0.0209298
$960$	−19.1882	−	12.8362i	−0.619296	−	0.414287i
$961$	28.9181			0.932843
$962$	−2.56320	+	6.57137i	−0.0826410	+	0.211869i
$963$	2.91678	−	2.91678i	0.0939920	−	0.0939920i
$964$	16.1916	+	14.8979i	0.521495	+	0.479828i
$965$	61.4410	−	4.37234i	1.97786	−	0.140750i
$966$	−0.509700	−	1.16160i	−0.0163993	−	0.0373740i
$967$	21.2528	+	21.2528i	0.683442	+	0.683442i	0.960774	−	0.277332i	$-0.0894501\pi$
$967$	21.2528	+	21.2528i	0.683442	+	0.683442i	−0.277332	+	0.960774i	$0.589450\pi$
$968$	2.54057	−	1.24319i	0.0816569	−	0.0399577i
$969$		−	4.89056i		−	0.157107i
$970$	1.70154	+	0.527956i	0.0546332	+	0.0169516i
$971$			40.2688i			1.29229i	0.763215	+	0.646144i	$0.223619\pi$
$971$			40.2688i			1.29229i	−0.763215	+	0.646144i	$0.776381\pi$
$972$	25.2418	−	1.05035i	0.809630	−	0.0336900i
$973$	−1.28238	−	1.28238i	−0.0411114	−	0.0411114i
$974$	19.7090	−	8.64813i	0.631518	−	0.277104i
$975$	−0.611442	−	4.27430i	−0.0195818	−	0.136887i
$976$	2.34920	+	28.1788i	0.0751962	+	0.901983i
$977$	23.6559	−	23.6559i	0.756819	−	0.756819i	−0.218923	−	0.975742i	$-0.570255\pi$
$977$	23.6559	−	23.6559i	0.756819	−	0.756819i	0.975742	+	0.218923i	$0.0702545\pi$
$978$	−15.3202	−	5.97575i	−0.489886	−	0.191083i
$979$	5.69673			0.182068
$980$	3.51417	+	31.0687i	0.112256	+	0.992453i
$981$	12.6927			0.405248
$982$	22.5327	+	8.78902i	0.719047	+	0.280469i
$983$	−2.53162	+	2.53162i	−0.0807461	+	0.0807461i	−0.746326	−	0.665580i	$-0.768184\pi$
$983$	−2.53162	+	2.53162i	−0.0807461	+	0.0807461i	0.665580	+	0.746326i	$0.268184\pi$
$984$	6.08475	−	17.7460i	0.193975	−	0.565723i
$985$	−3.08361	−	43.3316i	−0.0982521	−	1.38066i
$986$	−11.0111	+	4.83156i	−0.350665	+	0.153868i
$987$	0.941375	+	0.941375i	0.0299643	+	0.0299643i
$988$	0.147502	+	3.54472i	0.00469266	+	0.112773i
$989$		−	43.2194i		−	1.37430i
$990$	1.96572	+	3.73433i	0.0624746	+	0.118685i
$991$		−	14.9715i		−	0.475586i	−0.971316	−	0.237793i	$-0.923576\pi$
$991$		−	14.9715i		−	0.475586i	0.971316	−	0.237793i	$-0.0764240\pi$
$992$	2.32403	−	7.82423i	0.0737881	−	0.248420i
$993$	9.34206	+	9.34206i	0.296461	+	0.296461i
$994$	0.0945102	+	0.215388i	0.00299768	+	0.00683170i
$995$	13.7147	−	15.8162i	0.434784	−	0.501406i
$996$	29.4509	−	32.0083i	0.933186	−	1.01422i
$997$	23.1266	−	23.1266i	0.732426	−	0.732426i	−0.238674	−	0.971100i	$-0.576713\pi$
$997$	23.1266	−	23.1266i	0.732426	−	0.732426i	0.971100	+	0.238674i	$0.0767127\pi$
$998$	7.02387	−	18.0073i	0.222337	−	0.570011i
$999$	−41.6947			−1.31916

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instead) (See

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.l.d.23.9	yes	28
4.3	odd	2		220.2.l.c.23.13	✓	28
5.2	odd	4		220.2.l.c.67.13	yes	28
20.7	even	4	inner	220.2.l.d.67.9	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.l.c.23.13	✓	28	4.3	odd	2
220.2.l.c.67.13	yes	28	5.2	odd	4
220.2.l.d.23.9	yes	28	1.1	even	1	trivial
220.2.l.d.67.9	yes	28	20.7	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	220.2.l.d.23.9

Level	$220$
Weight	$2$
Character	220.23
Analytic conductor	$1.757$
Analytic rank	$0$
Dimension	$28$
Inner twists	$2$